New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2025 · 22 Jan · Shift 1 · Q39

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 22 Jan · Shift 1 · Q39

Definite Integration question

2025 · 22 Jan · Shift 1 · Q39

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let for

f(x)=7 \tan ^8 x+7 \tan ^6 x-3 \tan ^4 x-3 \tan ^2 x, \quad \mathrm{I}_1=\int_0^{\pi / 4} f(x) \mathrm{d} x

and

\mathrm{I}_2=\int_0^{\pi / 4} x f(x) \mathrm{d} x

. Then

7 \mathrm{I}_1+12 \mathrm{I}_2

is equal to :

A
2 $\pi$
B
1
C
$\pi$
D
2

More from Definite Integration

The value of $\int_{e^{2}}^{e^{4}} \frac{1}{x} (\frac{e ^{((l o g_{e} x)^{2} + 1)^{- 1}}}{e ^{((l o g_{e} x)^{2} + 1)^{- 1}} + e ^{((6 - l o g_{e} x)^{2} + 1)^{- 1}}}) d x$ is2025 · MCQ
If $I = \int_{0}^{\frac{π}{2}} \frac{s i n ^{\frac{3}{2}} x}{s i n ^{\frac{3}{2}} x + c o s ^{\frac{3}{2}} x} d x$ , then $\int_{0}^{2 I} \frac{x s i n x c o s x}{s i n ^{4} x + c o s ^{4} x} d x$ equals :2025 · MCQ
If $I (m, n) = \int_{0}^{1} x^{m - 1} (1 - x)^{n - 1} d x, m, n > 0$ , then $I (9, 14) + I (10, 13)$ is2025 · MCQ
If $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{96 x ^{2} c o s ^{2} x}{( 1 + e ^{x} )} d x = π (α π^{2} + β), α, β \in Z$ , then $(α + β)^{2}$ equals2025 · MCQ
Let $f : R \to R$ be a twice differentiable function such that $f (2) = 1$ . If $F (x) = x f (x)$ for all $x \in R$ , $0 \int 2 x F^{'} (x) d x = 6$ …2025 · MCQ
Let $f$ be a real valued continuous function defined on the positive real axis such that $g (x) = 0 \int x t f (t) d t$ . If $g (x^{3}) = x^{6} + x^{7}$ , then value of $r = 1 \sum 15 f (r^{3})$ is :2025 · MCQ
The integral $80 0 \int \frac{π}{4} (\frac{s i n θ + c o s θ}{9 + 16 s i n 2 θ}) d θ$ is equal to :2025 · MCQ
Let $f : (0, \infty) \to R$ be a twice differentiable function. If for some $a e 0, 0 \int 1 f (λ x) d λ = a f (x), f (1) = 1$ and $f (16) = \frac{1}{8}$ , then $16 - f^{'} (\frac{1}{16})$ …2025 · Numerical