Advertisements
Advertisements
Question
Evaluate the following using properties of definite integral:
`int_(- pi/4)^(pi/4) x^3 cos^3 x "d"x`
Sum
Solution
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
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\limits_0^1 \frac{1}{1 + x^2} dx\]
\[\int\limits_0^1 \frac{x}{x + 1} dx\]
\[\int\limits_0^{\pi/2} \sin 2x \tan^{- 1} \left( \sin x \right) dx\]
\[\int_0^\pi \cos x\left| \cos x \right|dx\]
If f is an integrable function, show that
\[\int\limits_{- a}^a x f\left( x^2 \right) dx = 0\]
\[\int\limits_a^b \cos\ x\ dx\]
\[\int\limits_0^2 \left( x^2 + 2x + 1 \right) dx\]
\[\int\limits_{- \pi/2}^{\pi/2} x \cos^2 x\ dx .\]
\[\int\limits_0^2 \left[ x \right] dx .\]
\[\int\limits_1^5 \frac{x}{\sqrt{2x - 1}} dx\]
