integration-by-parts

The value of $x$ such that $x>1$, satisfying the equation $\int_1^x t \ln t d t=\frac{1}{4}$ is

The value of the integral given below is $$$\int_0^\pi {{x^2}\,\cos \,x\,dx} $$$

If $$\int_0^{2\pi } {\left| {x\sin x} \right|dx = k\pi ,} $$ then the values of $$k$$ is equal to _________ .

(a) Find the points of local maxima and minima, if any, of the following function defined $$0 \le x \le 6.\,\,\,{x^3} - 6{x^2} + 9x + 15$$ (b) Integrate $$\,\,\,\int\limits_{ - \pi...

The value of the double integral $$\int\limits_0^1 {\int\limits_x^{{1 \over x}} {{x \over {1 + {y^2}}}\,\,dx\,\,dy = \_\_\_\_\_.} } $$