WB JEE 2019 | Definite Integration Question 61 | Mathematics

WB JEE 2019

MCQ (More than One Correct Answer)

-0

Let $${I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx$$. If $${a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}$$ for all n $$ \ge $$ 1, then

a₁, a₂, a₃ are in GP

b₁, b₂, b₃ are in AP

c₁, c₂, c₃ are in HP

a₁, a₂, a₃ are in AP

WB JEE 2018

MCQ (More than One Correct Answer)

-0

Let $$I = \int\limits_0^I {{{{x^3}\cos 3x} \over {2 + {x^2}}}dx} $$, then

$$ - {1 \over 2} < I < {1 \over 2}$$

$$ - {1 \over 3} < I < {1 \over 3}$$

$$ - 1 < I < 1$$

$$ - {3 \over 2} < I < {3 \over 2}$$

WB JEE 2017

MCQ (More than One Correct Answer)

-0

Let f be a non-constant continuous function for all x $$ \ge $$ 0. Let f satisfy the relation f(x) f(a $$-$$ x) = 1 for some a $$ \in $$ R⁺. Then, $$I = \int_0^a {{{dx} \over {1 + f(x)}}} $$ is equal to

$${a \over 4}$$

$${a \over 2}$$

f(a)

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