Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 64

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Let $a = \int_{0}^{\frac{π}{2}} \frac{\sin x}{x} d x,$ then

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Important Questions on Definite Integrals and Their Properties

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IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 65

If

f (x) = \int_{0}^{x} \frac{e^{\cos t}}{e^{\cos t} + e^{- \cos t}} d t,

then

2 f (π) =

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 66

\int_{0}^{\sqrt{2}} [x^{2}] d x

is equal to

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 67

\int_{π}^{10 π} |\sin x| d x

is equal to

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 68

If

f (a + b - x) = f (x)

, then

\int_{a}^{b} x f (x) d x

is equal to

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 69

The value of

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

is

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 70

If

\int_{0}^{π} x f (\sin x) d x = A \int_{0}^{π / 2} f (\sin x) d x,

then

A

is

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 71

If $f (x) = \frac{e^{x}}{1 + e^{x}}, I_{1} = \int_{f (- a)}^{f (a)} x g (x (1 - x)) d x$ and $I_{2} = \int_{f (- a)}^{f (a)} g (x (1 - x)) d x,$ then $\frac{I_{2}}{I_{1}} =$

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Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 72

The value of the integral

\int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} d x

is