Consider the integral $\int_{0}^{\infty} \frac{\sin ^{2} x}{(1+x)^{2}} d x$ .Which if the following is true?
A)The integral converges with an upper bound of 0.
B)The integral converges with an upper bound of 1.
C)The integral diverges.

Question

Quizplus · Accepted Answer

The integral converges with an upper bound of 1 because the integrand $\frac{\sin^2 x}{(1+x)^2}$ is positive and bounded above by $\frac{1}{(1+x)^2}$ for all $x \geq 0$, and the integral of $\frac{1}{(1+x)^2}$ from 0 to infinity converges.

Consider the Integral ∫0∞sin⁡2x(1+x)2dx\int_{0}^{\infty} \frac{\sin ^{2} x}{(1+x)^{2}} d x∫0∞​(1+x)2sin2x​dx Which If the Following Is True? A)The Integral Converges with If

Consider the Integral $\int_{0}^{\infty} \frac{\sin ^{2} x}{(1+x)^{2}} d x$ Which If the Following Is True?
A)The Integral Converges with If