1

JEE Main 2021 (Online) 17th March Morning Shift

Numerical

+4

-1

If [ . ] represents the greatest integer function, then the value of

$$\left| {\int\limits_0^{\sqrt {{\pi \over 2}} } {\left[ {[{x^2}] - \cos x} \right]dx} } \right|$$ is ____________.

$$\left| {\int\limits_0^{\sqrt {{\pi \over 2}} } {\left[ {[{x^2}] - \cos x} \right]dx} } \right|$$ is ____________.

Your input ____

2

JEE Main 2021 (Online) 16th March Morning Shift

Numerical

+4

-1

Let the curve y = y(x) be the solution of the differential equation, $${{dy} \over {dx}}$$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $${{4\sqrt 8 } \over 3}$$, then the value of y(1) is equal to _________.

Your input ____

3

JEE Main 2021 (Online) 16th March Morning Shift

Numerical

+4

-1

Let f : R $$ \to $$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$$\in$$R.

If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I

If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I

_{1}+ 2I_{2}is equal to ____________.Your input ____

4

JEE Main 2021 (Online) 16th March Morning Shift

Numerical

+4

-1

If the normal to the curve y(x) = $$\int\limits_0^x {(2{t^2} - 15t + 10)dt} $$ at a point (a, b) is parallel to the line x + 3y = $$-$$5, a > 1, then the value of | a + 6b | is equal to ___________.

Your input ____

Questions Asked from Definite Integrals and Applications of Integrals (Numerical)

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