Mathematics Tes...

\(\smallint {e^x}\left\{ {f\left( x \right) + f'\left( x \right)} \right\}dx\;\) is equal to

What is \(\rm \int^\pi _0 ln\left(tan\frac{x}{2}\right) dx\) equal to?

What is \(\displaystyle\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \rm \dfrac{sin^5 \ x \ cos^3 \ x}{x^4}dx\) equal to?

A definite integral as a limit of a sum is given as \(\lim_{n \rightarrow \infty} \sum_{r = 0}^{r = n} \frac{1}{n} sin \left( \frac{r}{n} \right) dx\). What will be the value of this sum?

Evaluate: \(\rm \int_{-\pi/2}^{\pi/2}|\sin x|\ dx\)

The differentiation of Integral \(I = \rm \int_{\sin x}^{\cos x} \log t^2 \ dt\) with respect to x at x = π/4?

If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is \(\mathop \smallint \nolimits_0^{\rm{a}} {\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right){\rm{dx}}\) equal to?

Find the value of \(\rm \int{ {cos2x}\over {cosx} }dx\)

If \(\int_{0}^{\frac{\pi}{2}}\frac{sinx}{sinx\ +\ cosx}dx\ =\ g''(x)\ +\ C\)  where g'(1) = 1 then C will be

What is \(\rm \displaystyle\int e^{\log x} \sin x \ dx\) equal to ?