The value of -11 2 - x - - x -3 dx is

∫_ 1^1 ( 2 | x | | x |^3 )dx = 2∫_0^1 ( 2 | x | | x |^3 )dx (∵ integrand is an even function) =2∫_0^1(2x x^3)dx=2 [ x^2 x^4/4 ]_0^1 =2 [ 1 1/4 ]=2 ( 3/ ...

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Standard XII

Mathematics

Property 1

The value of ...

Question

The value of $\int_{- 1}^{1} (2 | x | - {| x |}^{3}) d x$ is

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3/4

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3/2

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Solution

The correct option is C
3/2

$\int_{- 1}^{1} (2 | x | - {| x |}^{3}) d x = 2 \int_{0}^{1} (2 | x | - {| x |}^{3}) d x$
( $∵$ integrand is an even function)
$= 2 \int_{0}^{1} (2 x - x^{3}) d x = 2 {[x^{2} - \frac{x^{4}}{4}]}_{0}^{2} = 2 [1 - \frac{1}{4}] = 2 (\frac{3}{4}) = \frac{3}{2}$

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The value of ∫1−1(2|x|−|x|3)dx is

The correct option is C 3/2 ∫1−1(2|x|−|x|3)dx=2∫10(2|x|−|x|3)dx (∵ integrand is an even function) =2∫10(2x−x3)dx=2[x2−x44]10=2[1−14]=2(34)=32

The value of $\int_{- 1}^{1} (2 | x | - {| x |}^{3}) d x$ is

The correct option is C
3/2

$\int_{- 1}^{1} (2 | x | - {| x |}^{3}) d x = 2 \int_{0}^{1} (2 | x | - {| x |}^{3}) d x$
( $∵$ integrand is an even function)
$= 2 \int_{0}^{1} (2 x - x^{3}) d x = 2 {[x^{2} - \frac{x^{4}}{4}]}_{0}^{2} = 2 [1 - \frac{1}{4}] = 2 (\frac{3}{4}) = \frac{3}{2}$