WB JEE 2017 | Definite Integration Question 72 | Mathematics

WB JEE 2017

MCQ (Single Correct Answer)

-0.5

If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to

$${1 \over 2}(1 - {x^2})$$

$$1 - {x^2}$$

$${1 \over 2}(1 + {x^2})$$

$$1 + {x^2}$$

WB JEE 2017

MCQ (Single Correct Answer)

-0.5

Let $$I = \int_0^{100\pi } {\sqrt {(1 - \cos 2x)} } \,dx$$, then

I = 0

I = 200$$\sqrt 2 $$

I = $$\pi$$$$\sqrt 2 $$

I = 100

WB JEE 2016

MCQ (Single Correct Answer)

-0.25

$$\int\limits_0^1 {\log \left( {{1 \over x} - 1} \right)} dx$$ is equal to

None of the above

WB JEE 2016

MCQ (Single Correct Answer)

-0.5

If [x] denotes the greatest integer less than or equal to x, then the value of the integral $$\int\limits_0^2 {{x^2}[x]\,dx} $$ equals

$${5 \over 3}$$

$${7 \over 3}$$

$${8 \over 3}$$

$${4 \over 3}$$

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