Advertisements
Advertisements
प्रश्न
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "d"x`
बेरीज
Advertisements
उत्तर
`int_0^oo "e"^(-4x) x^4 "d"x = int_0^oo x^"n" "e"^(-ax) "d"x`
`("n"!)/("a"^("n" + 1))`
Where n = 4
a = 4
So the integral becomes `(4!)/4^5 = (4 xx 3 xx 2)/(4 xx 4 xx 4 xx 4 xx 4)`
= `3/128`
shaalaa.com
Definite Integrals
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Integral Calculus – 1 - Exercise 2.10 [पृष्ठ ५१]
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^{\pi/2} \left( \sin x + \cos x \right) dx\]
\[\int\limits_1^2 e^{2x} \left( \frac{1}{x} - \frac{1}{2 x^2} \right) dx\]
\[\int\limits_0^{\pi/2} 2 \sin x \cos x \tan^{- 1} \left( \sin x \right) dx\]
\[\int\limits_{- a}^a \sqrt{\frac{a - x}{a + x}} dx\]
\[\int\limits_0^\infty \frac{\log x}{1 + x^2} dx\]
\[\int\limits_0^\pi \frac{x}{1 + \cos \alpha \sin x} dx, 0 < \alpha < \pi\]
If f(2a − x) = −f(x), prove that
\[\int\limits_0^{2a} f\left( x \right) dx = 0 .\]
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
Write the coefficient a, b, c of which the value of the integral
\[\int\limits_{- 3}^3 \left( a x^2 + bx + c \right) dx\] is independent.
Given `int "e"^"x" (("x" - 1)/("x"^2)) "dx" = "e"^"x" "f"("x") + "c"`. Then f(x) satisfying the equation is:
