JEE Main 2021 (Online) 26th February Evening Shift | Definite Integration Question 130 | Mathematics

JEE Main 2021 (Online) 26th February Evening Shift

MCQ (Single Correct Answer)

-1

Let $$f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}} $$ be a differentiable function for all x$$\in$$R. Then f(x) equals :

$${e^{({e^{x - 1}})}}$$

$$2{e^{{e^x}}} - 1$$

$$2{e^{{e^x} - 1}} - 1$$

$${e^{{e^x}}} - 1$$

JEE Main 2021 (Online) 26th February Evening Shift

MCQ (Single Correct Answer)

-1

For x > 0, if $$f(x) = \int\limits_1^x {{{{{\log }_e}t} \over {(1 + t)}}dt} $$, then $$f(e) + f\left( {{1 \over e}} \right)$$ is equal to :

$${1 \over 2}$$

$$-$$1

JEE Main 2021 (Online) 26th February Morning Shift

MCQ (Single Correct Answer)

-1

The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\cos }^2}x} \over {1 + {3^x}}}} dx$$ is :

$$2\pi $$

$${\pi \over 2}$$

$$4\pi $$

$${\pi \over 4}$$

JEE Main 2021 (Online) 26th February Morning Shift

MCQ (Single Correct Answer)

-1

The value of $$\sum\limits_{n = 1}^{100} {\int\limits_{n - 1}^n {{e^{x - [x]}}dx} } $$, where [ x ] is the greatest integer $$ \le $$ x, is :

100e

100(e $$-$$ 1)

100(1 + e)

100(1 $$-$$ e)

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