Integrals -zambak- [work] -

Find ( \int (3x^2 + 4\sin x) , dx ). Integrate term by term. ( \int 3x^2 , dx = x^3 ) and ( \int 4\sin x , dx = -4\cos x ). Hence, ( \int (3x^2 + 4\sin x) , dx = x^3 - 4\cos x + C ). (Margin Note: Differentiate your answer to check your work!)

The book includes a unique "Historical Corner" here, crediting Newton and Leibniz, and shows how the FTC allows us to compute exact areas without sums of infinite rectangles. Integrals -Zambak-

The latter part of the chapter challenges students with: Find ( \int (3x^2 + 4\sin x) , dx )