Statement-I: The value of the integral ∫ π 6 π 3 d x 1 + tan x is equal to π 6 . Statement-II: ∫ a b f x d x = ∫ a b f a + b - x d x .

Statement - I is false; Statement - II is true

Statement - I is true; Statement - II is true; Statement - II is a correct explanation for Statement - I

Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I

Statement - I is true; Statement - II is false

Statement-I: The value of the integral ∫ π 6 π 3 d x 1 + tan x is equal to π 6 . Statement-II: ∫ a b f x d x = ∫ a b f a + b - x d x .

Statement - I is false; Statement - II is true

Statement - I : The value of the integral ∫ π / 6 π / 3 d x 1 + tan x is equal to π 6 . Statement - II : ∫ a b f x d x = ∫ a b f a + b - x d x .

Statement - I is false; Statement - II is true.

Statement - I is true; Statement - II is false.

Statement - I true; Statement - II is true; Statement - II is a correct explanation for Statement - I .

Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I .

Define g x = ∫ - 3 3 f x - y f y d y , for all real x , where f t = 1 , 0 ≤ t ≤ 1 0 , e l s e w h e r e , then

g x is continuous everywhere and differentiable everywhere except at x = 0 , 1 , 2

g x is not continuous everywhere

g x is continuous everywhere but differentiable nowhere

g x is continuous everywhere and differentiable everywhere except at x = 0, 1

HARD

Earn 100

Statement-I: The value of the integral $\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{1 + \sqrt{\tan x}}$ is equal to $\frac{π}{6} .$

Statement-II: $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .$

7.84% studentsanswered this correctly

Important Questions on Integrals

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The value of

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{x^{2} \cos x}{1 + e^{x}} d x

is equal to

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

\int_{- 1}^{1} \log (x + \sqrt{x^{2} + 1}) d x

is equal to

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The integral

\int_{2}^{4} \frac{log x^{2}}{log x^{2} + log {(6 - x)}^{2}} d x

is equal to

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The integral

\int_{0}^{π} \sqrt{1 + 4 {sin}^{2} \frac{x}{2} - 4 sin \frac{x}{2}} d x

equals

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Statement - I : The value of the integral $\int_{π / 6}^{π / 3} \frac{d x}{1 + \sqrt{\tan x}}$ is equal to $\frac{π}{6} .$

Statement - II : $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .$

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Let

f : R \to R

be a function such that

f (2 - x) = f (2 + x)

and

f (4 - x) = f (4 + x)

, for all

x \in R

and

\int_{0}^{2} f (x) d x = 5

. Then the value of

\int_{10}^{50} f (x) d x

EASY

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

\int_{0}^{π} e^{\sin^{2} x} \cos^{3} x d x

is equal to

EASY

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

\int_{0}^{3} [x] d x =______,

where

[x]

is greatest integer function

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Let

f (x) = \int_{0}^{x} g (t) d t,

where

g

is a non-zero even function. If

f (x + 5) = g (x),

then

\int_{0}^{x} f (t) d t

equals

EASY

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The value of

\int_{0}^{2 π} [\sin 2 x (1 + \cos 3 x)] d x

, where

[t]

denotes the greatest integer function is

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Let

f (x) = \max \{3, x^{2}, \frac{1}{x^{2}}\}

for

\frac{1}{2} \leq x \leq 2 .

Then the value of the integral

\int_{\frac{1}{2}}^{2} f (x) d x

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The value of

\int_{0}^{π / 2} \frac{{s i n}^{3} x}{s i n x + c o s x} d x

is:

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Define

g (x) = \int_{- 3}^{3} f (x - y) f (y) d y,

for all real

x,

where

f (t) = \{\begin{matrix} 1, & 0 \leq t \leq 1 \\ 0, & e l s e w h e r e \end{matrix},

then

EASY

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

Let

f

and

g

be continuous functions on

[0, a]

such that

f (x) = f (a - x)

and

g (x) + g (a - x) = 4

, then

\int_{0}^{a} f (x) g (x) d x

is equal to

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

\int_{0}^{\frac{π}{2}} \log \cos x d x = \frac{π}{2} \log (\frac{1}{2}),

then

\int_{0}^{\frac{π}{2}} \log \sec x d x =

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The integral value of

\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{x}{1 + \sin x} d x =

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The integral value of

\int_{0}^{\frac{π}{2}} \frac{2^{\sin x}}{2^{\sin x} + 2^{\cos x}} d x =

HARD

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

\int_{- 1}^{1} \frac{x^{3} + |x| + 1}{x^{2} + 2 |x| + 1} d x

is equal to

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

f (x) = \frac{2 - x c o s x}{2 + x c o s x}

and

g (x) = \log_{e} x,

then the value of the integral

\int_{- \frac{π}{4}}^{\frac{π}{4}} g (f (x)) d x

MEDIUM

Mathematics>Integral Calculus>Integrals>Some Properties of Definite Integrals

The value of the integral

\int_{- π}^{π} \frac{{c o s}^{2} x}{1 + a^{x}} d x,

a > 0

Statement-I: The value of the integral ∫π6π3dx1+tanx is equal to π6. Statement-II: ∫abfxdx=∫abfa+b-xdx.

Important Questions on Integrals

Learn and Prepare for any exam you want !

Statement-I: The value of the integral $\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{1 + \sqrt{\tan x}}$ is equal to $\frac{π}{6} .$

Statement-II: $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .$