![5. a) Evaluate st -2x + 7x? dx. b) Evaluate: [** sin(x* +1]dx. c) Evaluate: [(3x? –5x+4-4e”)dx](http://img.homeworklib.com/questions/ce8c8650-04e5-11eb-9492-533ea2e88d6a.png?x-oss-process=image/resize,w_560)
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5. a) Evaluate st -2x + 7x? dx. b) Evaluate: [** sin(x*...
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...
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X...
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X = c) lim X+0 4x2-3r d) lim a "270 3x - 3xcos(2x) 2x2 sin(3x)
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5)...
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
Evaluate the integral. 5 cost 3x dx 15 5 5 0 5x+7 sin 6x + 32...
Evaluate the integral. 5 cost 3x dx 15 5 5 0 5x+7 sin 6x + 32 sin 12x + C 15 5 O Š x + 12 sin 6x + sin 12x + C 5. Tx+ 12 sin 3x + sin 12x + C 15 5 5 Tx+ 12 sin 3x + 56 sin 6x + C
Problem 6 Evaluate: dx 16 - 22 Hints: sin²x = 1 - cos(2.0) and sin(2x) =...
Problem 6 Evaluate: dx 16 - 22 Hints: sin²x = 1 - cos(2.0) and sin(2x) = 2 sin c cos r. 2 (Show all details.)
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]....
1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]. b) Find the antiderivatives: i) sin(2x) dx ii) (cos(4x)+3x^2) dx
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx...
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bou...
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1, y-x +4 y#2x+2y»2x + 5 A) -5 B) 10 C)5 D)-10 32) y+ x where R is the trapezoid with vertices at (6,0), ,0).。. 6), (0.9) 45 45 B) ÷ sin l 45 C) sin 2 45 A) sin 2
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1,...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7....
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y =...
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
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...
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X = c) lim X+0 4x2-3r d) lim a "270 3x - 3xcos(2x) 2x2 sin(3x)
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
Evaluate the integral. 5 cost 3x dx 15 5 5 0 5x+7 sin 6x + 32 sin 12x + C 15 5 O Š x + 12 sin 6x + sin 12x + C 5. Tx+ 12 sin 3x + sin 12x + C 15 5 5 Tx+ 12 sin 3x + 56 sin 6x + C
Problem 6 Evaluate: dx 16 - 22 Hints: sin²x = 1 - cos(2.0) and sin(2x) = 2 sin c cos r. 2 (Show all details.)
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1, y-x +4 y#2x+2y»2x + 5 A) -5 B) 10 C)5 D)-10 32) y+ x where R is the trapezoid with vertices at (6,0), ,0).。. 6), (0.9) 45 45 B) ÷ sin l 45 C) sin 2 45 A) sin 2
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1,...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
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