$\smallint \,\,\sin \,\,x{\rm{ }}d\,\,(\cos \,\,x)$ is equal to

$\sin \,\,x\,\, + \,\,\cos \,\,x + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\sin \,\,x\mathrm{ }d\,\,(\cos \,\,x)

is equal to

View answer and explanation

Correct option: B

\frac{1}{4}\,\,\sin \,\,2x\,\, - \,\,\frac{x}{2}\,\, + \,\,c

Option B (

\frac{1}{4}\,\,\sin \,2x\, - \,\frac{x}{2}\, + \,c

) is correct because it is the result of integrating sin(x) d(cos(x)) using substitution and trigonometric identities.

Practice All Chapter MCQs →

\int \sin ^5 x \cos ^4 x d x=

f(x)

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f\left(\frac{4}{25}\right)

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

f(1)

{C}

\int \frac{x^7}{\left(1-x^2\right)^5} d x

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx