Which function is an antiderivative of $\cos x$?
A$\tan x$
B$-\sin x$
C$-\cos x$
D$\sin x$
Answer & Solution
Correct answer: D. $\sin x$
1. An antiderivative $F$ of $f$ satisfies $F'(x)=f(x)$.
2. We need $F$ with $F'(x)=\cos x$.
3. Since $\dfrac{d}{dx}(\sin x)=\cos x$, the antiderivative is $\sin x$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.289_
Related questions
$\displaystyle\int_2^3 \dfrac{x\,dx}{x^2+1}$ equals$\displaystyle\int_0^{2a} f(x)\,dx$ equals $2\displaystyle\int_0^{a} f(x)\,dx$ precisely wIf $f(a+b-x)=f(x)$, then $\displaystyle\int_a^b x\,f(x)\,dx$ is equal to$\displaystyle\int \frac{dx}{e^{x}+e^{-x}}$ is equal toA rational function $\dfrac{P(x)}{Q(x)}$ is called proper when$\displaystyle\int_0^{\pi/4} \tan x\,dx$ equals$\displaystyle\int_0^{1} x e^{x^2}\,dx$ equalsThe value of $\displaystyle\int_0^{\pi/2} \log\!\left(\dfrac{4+3 in x}{4+3\cos x}\right)dx