int {x cos(x^2) , dx} is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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

Similar Questions

$\int \frac{\sin x \cdot \cos x}{\sin ^{4} x+\cos ^{4} x} d x=$

$\int \frac{(1-\cos x)^{2 / 7}}{(1+\cos x)^{9 / 7}} d x=$

$\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=$

$\int \frac{dx}{(a^2 + x^2)^{3/2}}$ is equal to

$\int \frac{2 \tan (x)}{1+2 \tan ^2(x)} d x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module