Which of the following integrals can be best evaluated using integration by parts?

Question

Which of the following integrals can be best evaluated using integration by parts?

A. ∫ $x sin (x^{2})$ $xsin(x^2)$ dx
B. ∫ $x^{2} sin (x)$ $x^2sin(x)$ dx
C. ∫ ${sin}^{2} (x)$ $sin^2(x)$ dx

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Answer 1 · 2017-06-14T04:39:21

$\int x^{2} sin (x)$ $∫ x^2sin(x)$ dx

Explanation:

$\int x^{2} sin (x)$ $∫ x^2sin(x)$ dx can only be done using integration by parts. It is a product of 2 distinct functions and a u-sub does not simplify the integral.

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Which of the following integrals can be best evaluated using integration by parts?

A. ∫ $x sin (x^{2})$ $xsin(x^2)$ dx
B. ∫ $x^{2} sin (x)$ $x^2sin(x)$ dx
C. ∫ ${sin}^{2} (x)$ $sin^2(x)$ dx

1 Answer

Explanation:

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Which of the following integrals can be best evaluated using integration by parts?

A. ∫ xsin(x2)xsin(x^2)dx B. ∫ x2sin(x)x^2sin(x) dx C. ∫ sin2(x)sin^2(x) dx

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Explanation:

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A. ∫ $x sin (x^{2})$ $xsin(x^2)$ dx
B. ∫ $x^{2} sin (x)$ $x^2sin(x)$ dx
C. ∫ ${sin}^{2} (x)$ $sin^2(x)$ dx