Question

$\int\limits^a_b {x} \, dx 5x$

Answer 1

$\large\boxed{\begin{array}{l}\displaystyle\rm\int _a^b5x\,x\,dx=5\int_a^b x^2\,dx\\\rm\bigg[5\cdot\dfrac{1}{2}x^2\bigg]_a^b\\\\\rm\bigg[\dfrac{5}{2}x^2\bigg]_a^b=\dfrac{5}{2}\cdot b^2-\dfrac{5}{2}\cdot a^2\\\\\displaystyle\rm\int _a^b 5x\,x\,dx=\dfrac{5}{2}(b^2-a^2)\end{array}}$