Engineering Mat...

\(\underset{-\pi }{\overset{\pi }{\mathop \int }}\,cos\left( t \right)\cos \left( 3t \right)dt=\)

Find the value of the given function f?

\(f = \mathop \smallint \limits_0^{\sqrt {\frac{\pi }{2}} } xsin({x^2})\;dx\)

The value of the integral \(\mathop \smallint \limits_0^3 \frac{{2x}}{{{{\left( {1 - {x^2}} \right)}^{2/3}}}}dx\) is

The value of \(\mathop \smallint \limits_0^{\frac{\pi }{2}} \frac{{\sqrt {\sin x} }}{{\sqrt {\sin x} + \sqrt {\cos x} }}dx\) is

\(I = \mathop \smallint \limits_0^\infty \frac{{dx}}{{{{\left( {{x^2} + 1} \right)}^2}}}\) has the value

The value of \(\mathop \smallint \nolimits_0^{\frac{\pi }{2}} {\sin ^9}xdx\;\)is ____.

Note: correct upto 2 decimal places.

If \(f\left( x \right) = A~\cos\left( {\frac{{2\pi x}}{5}} \right) + C,\;f'\left( {\frac{{15}}{4}} \right) = \frac{1}{2}\) and \(\mathop \smallint \nolimits_0^5 f\left( x \right)dx = \frac{{A\pi }}{2}\) then the value of A and C are respectively.

The value of the integral \(\underset{a}{\overset{\text{ }\!\!b\!\!\text{ }}{\mathop \int }}\,\text{x}{{\cos }^{2}}\text{xdx}\) is\(\frac{{{\pi }^{2}}}{4}. \)

What is the correct value of a and b?

If \(\mathop \smallint \limits_0^1 \frac{{{e^t}}}{{1 + t}}dt = a\), then \(\mathop \smallint \limits_0^1 \frac{{{e^t}}}{{{{\left( {1 + t} \right)}^2}}}dt = \)

What is the value of \(\mathop \smallint \limits_0^{\frac{\pi }{2}} {\sin ^7}x{\cos ^5}x dx\)?