CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Let

F(x)=\dfrac{x^{5}}{5}-\cos x

. (a) Differentiate

F

with respect to

x

and state the resulting expression. (b) Explain how your result in part (a) establishes that

F

is an antiderivative of

x^{4}+\sin x

. (c) Describe, without further calculation, the complete family of antiderivatives of

x^{4}+\sin x

. Include a brief justification for your description.