1

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

Let $$F:[3,5] \to R$$ be a twice differentiable function on (3, 5) such that

$$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $$. If $$F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$$, then $$\alpha$$ + $$\beta$$ is equal to _______________.

$$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $$. If $$F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$$, then $$\alpha$$ + $$\beta$$ is equal to _______________.

Your input ____

2

JEE Main 2021 (Online) 18th March Evening Shift

Numerical

+4

-1

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.

Your input ____

3

JEE Main 2021 (Online) 18th March Morning Shift

Numerical

+4

-1

Let f(x) and g(x) be two functions satisfying f(x

^{2}) + g(4 $$-$$ x) = 4x^{3}and g(4 $$-$$ x) + g(x) = 0, then the value of $$\int\limits_{ - 4}^4 {f{{(x)}^2}dx} $$ isYour input ____

4

JEE Main 2021 (Online) 17th March Evening Shift

Numerical

+4

-1

Let $${I_n} = \int_1^e {{x^{19}}{{(\log |x|)}^n}} dx$$, where n$$\in$$N. If (20)I

_{10}= $$\alpha$$I_{9}+ $$\beta$$I_{8}, for natural numbers $$\alpha$$ and $$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ equals to ___________.Your input ____

Questions Asked from Definite Integration (Numerical)

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