New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Indefinite Integrals question

2023 · 10 Apr · Shift 1 · Q24

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2023 · 10 Apr · Shift 1 · Q24

Indefinite Integrals question

2023 · 10 Apr · Shift 1 · Q24

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

If

I(x) = \int {{e^{{{\sin }^2}x}}(\cos x\sin 2x - \sin x)dx}

and

I(0) = 1

, then

I\left( {{\pi \over 3}} \right)

is equal to :

A
$- {e^{{3 \over 4}}}$
B
$- {1 \over 2}{e^{{3 \over 4}}}$
C
${e^{{3 \over 4}}}$
D
${1 \over 2}{e^{{3 \over 4}}}$

More from Indefinite Integrals

For $α, β, γ, δ \in N$ , if $\int ((\frac{x}{e})^{2 x} + (\frac{e}{x})^{2 x}) lo g_{e} x d x = \frac{1}{α} (\frac{x}{e})^{β x} - \frac{1}{γ} (\frac{e}{x})^{δ x} + C$ …2023 · MCQ
Let $I (x) = \int \frac{x + 7}{x} d x$ and $I (9) = 12 + 7 lo g_{e} 7$ . If $I (1) = α + 7 lo g_{e} (1 + 22)$ , then $α^{4}$ is equal to .2023 · Numerical
Let $f (x) = \int \frac{d x}{( 3 + 4 x ^{2} ) 4 - 3 x ^{2}}, ∣ x ∣0$ , then $α^{2} + β^{2}$ is equal to .2023 · Numerical
Let $f (x) = \int \frac{2 x}{( x ^{2} + 1 ) ( x ^{2} + 3 )} d x$ . If $f (3) = \frac{1}{2} (lo g_{e} 5 - lo g_{e} 6)$ , then $f (4)$ is equal to2023 · MCQ
If $\int sec 2 x - 1 d x = α lo g_{e} cos 2 x + β + cos 2 x (1 + cos \frac{1}{β} x) +$ constant, then $β - α$ is equal to .2023 · Numerical
$The integral \int \frac{( 1 - \frac{1}{3} ) ( c o s x - s i n x )}{( 1 + \frac{2}{3} s i n 2 x )} d x is equal to$ 2022 · MCQ
If $\int \frac{1}{x} \frac{1 - x}{1 + x} d x = g (x) + c$ , $g (1) = 0$ , then $g (\frac{1}{2})$ is equal to :2022 · MCQ
If $\int \frac{( x ^{2} + 1 ) e ^{x}}{( x + 1 ) ^{2}} d x = f (x) e^{x} + C$ , where C is a constant, then $\frac{d ^{3} f}{d x ^{3}}$ at x = 1 is equal to :2022 · MCQ