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(D) To evaluate the integral $I = \int x \cos(x^2) \, dx$,we use the method of substitution.Let $t = x^2$.Then,differentiating both sides with respect

Vedclass · Accepted Answer

$\frac{1}{2} \sin(x^2) + c$

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(D) To evaluate the integral $I = \int x \cos(x^2) \, dx$,we use the method of substitution.Let $t = x^2$.Then,differentiating both sides with respect to $x$,we get $dt = 2x \, dx$,which implies $x \, dx = \frac{1}{2} \, dt$.Substituting these into the integral,we get:$I = \int \cos(t) \cdot \frac{1}{2} \, dt$$I = \frac{1}{2} \int \cos(t) \, dt$$I = \frac{1}{2} \sin(t) + c$Substituting $t = x^2$ back into the expression,we get:$I = \frac{1}{2} \sin(x^2) + c$.Thus,the correct option is $D$.

$\int {x \cos(x^2) \, dx}$ is equal to

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