New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2020 · Shift 2 · Q35

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

PYQ Library
JEE Advanced
Mathematics
Definite Integration
2020 · Shift 2 · Q35

Definite Integration question

2020 · Shift 2 · Q35

JEE AdvancedMathematicsDefinite IntegrationNumerical+4 / −1

Let

f:R \to R

be a differentiable function such that its derivative f' is continuous and f(

\pi

) =

-

6. If

F:[0,\pi ] \to R

is defined by

F(x) = \int_0^x {f(t)dt}

, and if

\int_0^\pi {(f'(x)} + F(x))\cos x\,dx

= 2 then the value of f(0) is ...........

Numerical answer

More from Definite Integration

If $I = \frac{2}{π} - π /4 \int π /4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - c o s 2 x )}$ , then 27I2 equals .................2019 · Numerical
The value of the integral $0 \int π /2 \frac{3 c o s θ}{( c o s θ + s i n θ ) ^{5}} d θ$ equals ..............2019 · Numerical
The value of the integral $\int_{0}^{1/2} \frac{1 + 3}{( ( x + 1 ) ^{2} ( 1 - x ) ^{6} ) ^{1/4}} d x$ is ........2018 · Numerical
If $I = \sum o l imi t s_{k = 1}^{98} \int_{k}^{k + 1} \frac{k + 1}{x ( x + 1 )} d x$ , then2017 · Multiple correct
The total number of distinct $x \in [0, 1]$ for which $0 \int x \frac{t ^{2}}{1 + t ^{4}} d t = 2 x - 1$ 2016 · Numerical
Let $f (x) = n \to \infty lim (\frac{n ^{n} ( x + n ) ( x + \frac{n}{2} ) ... ( x + \frac{n}{n} )}{n ! ( x ^{2} + n ^{2} ) ( x ^{2} + \frac{n ^{2}}{4} ) .... ( x ^{2} + \frac{n ^{2}}{n ^{2}} )})^{\frac{x}{n}},$ …2016 · Multiple correct
The value of $- \frac{π}{2} \int \frac{π}{2} \frac{x ^{2} c o s x}{1 + e ^{x}} d x$ is equal to2016 · MCQ
Let $f : R \to R$ be a function defined by $f (x) = {[x], 0, x \leq 2 x > 2$ where $[x]$ is the greatest integer less than or…2015 · Numerical