(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Question 5(10 marks)

Assume that a function f(x) is continuous on the interval [0,1].Express the following derivatives as formulae in terms of

[tex]x,f(x),f'(x) and \int_{a}^{x}f(t)dt[/tex]

[tex]a)\frac{d}{dx}\int_{x}^{0}tf(t)dt[/tex] [tex]b)\frac{d}{dx}\int_{0}^{x}xf(t)dt[/tex]

[tex]c)\frac{d}{dx}\int_{0}^{x}xf(x)dt[/tex]

3. The attempt at a solution

I got 6 marks from 10.Can you help me to find my mistakes?

a)[tex]xf(x)[/tex]

b)[tex]\frac{d}{dx}\int_{0}^{x}xf(t)dt=\int_{0}^{x}f(t)dt+x\frac{d}{dx}\int_{0}^{x}f

(t)dt=\int_{0}^{x}f(t)dt+xf(x)[/tex]

c)[tex]\frac{d}{dx}\int_{0}^{x}xf(x)dt=\int_{0}^{x}f(x)dt+f'(x)x\int_{0}^{x}dt+xf

(x)\frac{d}{dx}\int_{0}^{x}dt=f(x)x+f'(x)x^2+xf(x)=2xf(x)+x^2f'(x)[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: From Midterm exam.

**Physics Forums | Science Articles, Homework Help, Discussion**