Advertisements
Advertisements
प्रश्न
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
Advertisements
उत्तर
\[\int_{- \pi}^\pi x^{10} \sin^7 x d x\]
\[Let f\left( x \right) = x^{10} \sin^7 x\]
\[\text{Consider }f\left( - x \right) = \left( - x \right)^{10} \sin^7 \left( - x \right) = - x^{10} \sin^7 x = - f\left( x \right)\]
Hence f(x) is an odd function
Therefore
\[ \int_{- \pi}^\pi x^{10} \sin^7 x d x = 0\]
APPEARS IN
संबंधित प्रश्न
\[\int\limits_1^4 f\left( x \right) dx, where f\left( x \right) = \begin{cases}7x + 3 & , & \text{if }1 \leq x \leq 3 \\ 8x & , & \text{if }3 \leq x \leq 4\end{cases}\]
Evaluate the following integral:
Evaluate each of the following integral:
\[\int\limits_0^{2a} f\left( x \right) dx\] is equal to
Evaluate : \[\int\limits_0^\pi/4 \frac{\sin x + \cos x}{16 + 9 \sin 2x}dx\] .
\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\left( 1 + \cos x \right)^2} dx\]
\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]
\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]
\[\int\limits_0^{\pi/4} \cos^4 x \sin^3 x dx\]
\[\int\limits_1^3 \left| x^2 - 4 \right| dx\]
\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]
\[\int\limits_0^{\pi/2} \frac{\cos^2 x}{\sin x + \cos x} dx\]
\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]
Evaluate the following using properties of definite integral:
`int_(- pi/2)^(pi/2) sin^2theta "d"theta`
Choose the correct alternative:
The value of `int_(- pi/2)^(pi/2) cos x "d"x` is
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.
