- #1

KungPeng Zhou

- 22

- 7

- Homework Statement
- If f(x)=\int_{0}^{x}x^{2}\sin(t^{2})dt，find \frac{df(x)}{dx}

- Relevant Equations
- The Substitution Rule for Difinite Integrals，

The Fundamental Theorem of Calculus,

The Product Rule

From the question，we know that the variable is x

First，we can get

f(x)=x^{2}\int_{0}^{x}\sin(t^{2})dt，then\frac{df(x)}{dx}=2x\int_{0}^{x}\sin(t^{2})dt+x^{2}sint^{2}，but I can't deal with \int_{0}^{x}\sin(t^{2})dt，If I do the second differentiation, I can indeed deal with integrals, but there is a second derivative, and the problem is more complicated

First，we can get

f(x)=x^{2}\int_{0}^{x}\sin(t^{2})dt，then\frac{df(x)}{dx}=2x\int_{0}^{x}\sin(t^{2})dt+x^{2}sint^{2}，but I can't deal with \int_{0}^{x}\sin(t^{2})dt，If I do the second differentiation, I can indeed deal with integrals, but there is a second derivative, and the problem is more complicated