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Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1...
1- 2- 3- Tutorial Exercise Evaluate the indefinite integral. Vinter dx 1 + x18 Step 1...
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Tutorial Exercise Evaluate the indefinite integral. Vinter dx 1 + x18 Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in x8 dx for which the derivative is also present, though perhaps missing a constant 1 + x18 factor. 17 Finding u in this integral is a little trickier than in some others. We see that 1...
1- 2- Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We...
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Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in Jerez 42 + ex dx for which the derivative is also present. We see that 42 + ex is part of this integral, and the derivative of 42 + ex is ex et which is also present....
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
1. Begin by making the substitution u=ex . The resulting integral should be ripe for a trig substitution. 2. Make a cho...
1. Begin by making the substitution u=ex . The resulting
integral should be ripe for a trig substitution.
2. Make a choice of trig substitution based on the ±a2±b2u2 term
you see after the substitution. With the right choice, after
substituting and rewriting using sin/cos, you should again have
something fairly nice to solve as a trig integral.
3. The substitution sin(2θ)=2sin(θ)cos(θ) is useful after you
integrate.
4. Don’t forget to back substitute (through several
substitutions!) until everything is in...
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it....
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -VX 47 e dx х Step 1 00 х dx = 47 e dx can be evaluated using the 47 1 х substitution u = b lim b→ 1 x and du = Tx dx. Submit Skip (you cannot come back)
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x)...
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
13. Evaluate: (emcos x dx. Hint: Notice we see sin x and its derivative cosx. u=sin...
13. Evaluate: (emcos x dx. Hint: Notice we see sin x and its derivative cosx. u=sin x is a good choice for substitution. 14. Evaluated as 15. Evaluate: x cos(x") sin(x)dx. Hint: Since the cosine function is taken to the 4n power, try u = cos(x).
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of...
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it....
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -VX dx & e Step 1 - b е e 504 47 dx = lim b→ Ji 47 dx can be evaluated using the substitution u = x and VX 1 du = dx. 2V 2. Step 2 When x = 1 we have u = 1 and when x = b, we have b Vb Step 3 So lim b→ os 47 e...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Fi...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
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Tutorial Exercise Evaluate the indefinite integral. Vinter dx 1 + x18 Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in x8 dx for which the derivative is also present, though perhaps missing a constant 1 + x18 factor. 17 Finding u in this integral is a little trickier than in some others. We see that 1...
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2-
Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in Jerez 42 + ex dx for which the derivative is also present. We see that 42 + ex is part of this integral, and the derivative of 42 + ex is ex et which is also present....
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
1. Begin by making the substitution u=ex . The resulting
integral should be ripe for a trig substitution.
2. Make a choice of trig substitution based on the ±a2±b2u2 term
you see after the substitution. With the right choice, after
substituting and rewriting using sin/cos, you should again have
something fairly nice to solve as a trig integral.
3. The substitution sin(2θ)=2sin(θ)cos(θ) is useful after you
integrate.
4. Don’t forget to back substitute (through several
substitutions!) until everything is in...
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -VX 47 e dx х Step 1 00 х dx = 47 e dx can be evaluated using the 47 1 х substitution u = b lim b→ 1 x and du = Tx dx. Submit Skip (you cannot come back)
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
13. Evaluate: (emcos x dx. Hint: Notice we see sin x and its derivative cosx. u=sin x is a good choice for substitution. 14. Evaluated as 15. Evaluate: x cos(x") sin(x)dx. Hint: Since the cosine function is taken to the 4n power, try u = cos(x).
Explain how to compute the surface integral of scalar-valued function f over a sphere using an explicit description of the sphere. Choose the correct answer below. 2 h O A. Compute f(a cos u,a sin u,v)a sin u dv du 0 0 2Tt h O B. Compute f(a cos u,a sin u,v) dv du. 0 0 2 O C. Compute f(a sin u cos v,a sin u sin v,a cos u) dv du. 0 0 2 S. O D. Compute...
Tutorial Exercise Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. -VX dx & e Step 1 - b е e 504 47 dx = lim b→ Ji 47 dx can be evaluated using the substitution u = x and VX 1 du = dx. 2V 2. Step 2 When x = 1 we have u = 1 and when x = b, we have b Vb Step 3 So lim b→ os 47 e...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
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