Question

Integrate completely with respect to x :
∫10(7−4x)2dx

Answer 1

∫10(7−4x)²dx=10∫(7−4x)²dx=10∫(49-56x+16x²)dx=10(∫49dx-56∫xdx+16∫x²dx)=10(49∫dx-56∫xdx+16∫x²dx)=10(49x-56x²/2+16x³/3)+C=490x-280x²+160x³/3+C, where C is an arbitrary real constant.