Advertisements
Advertisements
प्रश्न
Evaluate the following using properties of definite integral:
`int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x`
योग
Advertisements
उत्तर
Let f(x) = `x^3 cos^3x`
f(– x) = `(- x)^3 cos^3 (- x)`
= `- x^3 cos^3 x`
= `- "f"(x)`
Here f(– x) = – f(x)
∴ f(x) is an odd function
∴ `int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x` = 0
shaalaa.com
Definite Integrals
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^1 \frac{2x + 3}{5 x^2 + 1} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan x}\]
\[\int\limits_3^5 \left( 2 - x \right) dx\]
\[\int\limits_0^2 e^x dx\]
\[\int\limits_0^2 \left( x^2 - x \right) dx\]
Evaluate :
\[\int\limits_2^3 3^x dx .\]
\[\int\limits_0^{2\pi} \cos^7 x dx\]
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "d"x`
Choose the correct alternative:
The value of `int_(- pi/2)^(pi/2) cos x "d"x` is
Choose the correct alternative:
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is
