int cos ^{3} x cdot e^{log (sin x)} d x is eq | vedclass

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

Question

(B) Let $I = \int \cos ^{3} x \cdot e^{\log (\sin x)} d x$. Since $e^{\log (\sin x)} = \sin x$,the integral becomes $I = \int \cos ^{3} x \sin x d x$.

Vedclass · Accepted Answer

$-\frac{\cos ^{4} x}{4}+c$

Vedclass · Answer

(B) Let $I = \int \cos ^{3} x \cdot e^{\log (\sin x)} d x$. Since $e^{\log (\sin x)} = \sin x$,the integral becomes $I = \int \cos ^{3} x \sin x d x$. Let $u = \cos x$. Then $du = -\sin x d x$,which implies $\sin x d x = -du$. Substituting these into the integral,we get $I = \int u^{3} (-du) = -\int u^{3} du$. Integrating with respect to $u$,we get $I = -\frac{u^{4}}{4} + c$. Substituting back $u = \cos x$,we obtain $I = -\frac{\cos ^{4} x}{4} + c$.

$\int \cos ^{3} x \cdot e^{\log (\sin x)} d x$ is equal to

Similar Questions

The value of $\int \frac{\sin x - \cos x}{\sin x + \cos x} \,dx$ is

If $f(x)=\int \frac{x^2 \, dx}{(1+x^2)(1+\sqrt{1+x^2})}$ and $f(0)=0$,then $f(1)$ is

$\int \frac{d x}{(x+100) \sqrt{x+99}}=f(x)+c \Rightarrow f(x)$

If $f(x) = \int \frac{1}{x^{1/4}(1+x^{1/4})} dx$ and $f(0) = -6$,then $f(1)$ is equal to:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module