Calculus 2

Question

Question

Calculus 2

Which of the follow is an appropriate technique to evaluate the integral ∫xcos(3x)dx?

A) $LaTeX: \text{Use u-substitution with }u = x.$ $Use u-substitution with$ u = x .

B) $LaTeX: \text{Use u-substitution with }u = \cos(3x).$ $Use u-substitution with$ u = cos ⁡ ( 3 x ) .

C) $LaTeX: \text{Use Integration-by-Parts with }u = x\text{ and }dv = \cos(3x) dx.$ $Use Integration-by-Parts with$ u = x and d v = cos ⁡ ( 3 x ) d x .

D) $LaTeX: \text{Use Integration-by-Parts with }u = 3x\text{ and }dv = x dx.$ $Use Integration-by-Parts with$ u = 3 x and d v = x d x .

E) $LaTeX: \text{Use Integration-by-Parts with }u = x\text{ and }dv = dx.$

Calculus-2

Add a comment Improve this question Transcribed image text

Answer 1

Similar Homework Help Questions

Calculus 2

Consider ∫ ( cos ⁡ x ) 3 ( sin ⁡ x ) 2 d x . The appropriate integration technique is C .A) u -substitution with u = ( cos ⁡ x ) 3 . B) Integration by-parts with u = ( cos ⁡ x ) 3 and d v = ( sin ⁡ x ) d x . C) u -substitution with u = sin ⁡ ( x ) . D) u -substitution with u = cos ⁡ ( x ) . E) Integration by-parts with u = sin ⁡ ( x ) and d v = ( cos ⁡ x ) 3 d x . The expression that is equivalent to ∫ ( cos ⁡ x ) 3 ( sin ⁡ x ) 2 d x is V) .I) − ( cos ⁡ x ) 4 − 3 ∫ ( cos ⁡ x ) 3 sin ⁡ x d x II) − 3 ( sin ⁡ x ) 2 ( cos ⁡ x ) 2 + 3 ∫ ( cos ⁡ x ) 3 sin ⁡ x d x III) − ∫ u 3 d u IV) ∫ ( u 2 − u 4 ) d u V) ∫ ( u 3 − u 5 ) d u
Calculus 2

Consider ∫ ( cos ⁡ x ) 3 ( sin ⁡ x ) 2 d x . The appropriate integration technique is C .A) u -substitution with u = ( cos ⁡ x ) 3 . B) Integration by-parts with u = ( cos ⁡ x ) 3 and d v = ( sin ⁡ x ) d x . C) u -substitution with u = sin ⁡ ( x ) . D) u -substitution with u = cos ⁡ ( x ) . The expression that is equivalent to ∫ ( cos ⁡ x ) 3 ( sin ⁡ x ) 2 d x is V) .I) − ( cos ⁡ x ) 4 − 3 ∫ ( cos ⁡ x ) 3 sin ⁡ x d x II) − 3 ( sin ⁡ x ) 2 ( cos ⁡ x ) 2 + 3 ∫ ( cos ⁡ x ) 3 sin ⁡ x d x III) − ∫ u 3 d u IV) ∫ ( u 2 − u 4 ) d u V) ∫ ( u 3 − u 5 ) d u
(1 point) For each of the following integrals, select an integration technique that could be used...

(1 point) For each of the following integrals, select an integration technique that could be used to evaluate the integral. The same answer may occur more than once. x-4 dx 2x2 + 3x - 2 1 dx (4 - x2) sinh*(2x) dx l [ sinh | 28#3x-2 2x2 + 3x - 2 dx x2 - 4 Use a substitution u = 2x^2 Use a substitution x = 2sin(t) Use hyperbolic double angle formulae Use hyperbolic identities and a substitution u...

Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember...

Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) x3 dx, u = x4 – 5 5 Evaluate the indefinite integral. (Use C for the constant of integration.) X dx 1 + x20
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write...

(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...
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 integral by making the given substitution. (Use C for the constant of integration.) dt...

Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt u = 1 - 2t (1 - 20) [-/1 Points] DETAILS SCALC8 4.5.512.XP. Evaluate the definite integral. 5 V1 + 3x dx Love
please solve 21 and 25 only u want to use integration by parts to find J...

please solve 21 and 25 only u want to use integration by parts to find J (5.x - 7) (x - 1) 4 dx, which is the better choice for u: U = 5x – 7 or u = (x - 1) 4? Explain your choice and then integrate. B blems 15–28 are mixed—some require integration by parts, others can be solved with techniques considered earlier. ntegrate as indicated, assuming x > 0 whenever the natural logarithm function is involved....
Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember...

Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) Der dok, v=x3-4 - dx, u = x5 - 4 Need Help? Read It Talk to a Tutor

1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate...

1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =

Calculus 2

Homework Answers

Request Answer!