New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2022 · 29 Jun · Shift 1 · Q33

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 29 Jun · Shift 1 · Q33

Definite Integration question

2022 · 29 Jun · Shift 1 · Q33

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx}

, where [t] denotes greatest integer less than or equal to t, is equal to:

A
$-$ 3
B
$-$ 2
C
2
D
0

More from Definite Integration

Let f be a real valued continuous function on [0, 1] and $f (x) = x + 0 \int 1 (x - t) f (t) d t$ . Then, which of the following points (x, y) lies on the curve y = f(x) ?2022 · MCQ
If $0 \int 2 (2 x - 2 x - x^{2}) d x = 0 \int 1 (1 - 1 - y^{2} - \frac{y ^{2}}{2}) d y + 1 \int 2 (2 - \frac{y ^{2}}{2}) d y + I$ , then I equals2022 · MCQ
Let $f (t) = 0 \int t e^{x^{3}} (\frac{x ^{8}}{( x ^{6} + 2 x ^{3} + 2 ) ^{2}}) d x$ . If $f (1) + f^{'} (1) = α e - \frac{1}{6}$ , then the value of 150 $α$ is equal to .2022 · Numerical
Let f : R $\to$ R be a continuous function. Then $x \to \frac{π}{4} lim \frac{\frac{π}{4} 2 \int s e c ^{2} x f ( x ) d x}{x ^{2} - \frac{π ^{2}}{16}}$ is equal to :2021 · MCQ
Let $J_{n, m} = 0 \int \frac{1}{2} \frac{x ^{n}}{x ^{m} - 1} d x$ , $\forall$ n > m and n, m $\in$ N. Consider a matrix $A = [a_{ij}]_{3 \times 3}$ where $a_{ij} = {j_{6 + i, 3} - j_{i + 3, 3}, 0, i \leq j i > j$ …2021 · MCQ
The function f(x), that satisfies the condition $f (x) = x + 0 \int π /2 sin x . cos y f (y) d y$ , is :2021 · MCQ
Let f : R $\to$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x $\in$ R. If $I_{1} = 0 \int 8 f (x) d x$ and $I_{2} = - 1 \int 3 f (x) d x$ , then the value of I1 + 2I2 is equal to …2021 · Numerical
If the normal to the curve y(x) = $0 \int x (2 t^{2} - 15 t + 10) d t$ at a point (a, b) is parallel to the line x + 3y = $-$ 5, a > 1, then the value of | a + 6b | is equal to .2021 · Numerical