Basic calc, but I can't seem to figure it out!

f'(x)∈ℝ,f(1)=1,∫xf'(x)dx from 0 to 1 is 1. Find ∫f(x)dx from 0 to 1. I'd like to see the step-by-step method, please.

Question

Basic calc, but I can't seem to figure it out!

f'(x)∈ℝ,f(1)=1,∫xf'(x)dx from 0 to 1 is 1. Find ∫f(x)dx from 0 to 1. I'd like to see the step-by-step method, please.

anonymous · Answer

Have you tried using integration by parts?

anonymous · Answer

∫xf'(x)dx=xf(x)-∫f'(x)dx

anonymous · Answer

Facepalm moment, haha.

Thanks.

anonymous · Answer

.-)

turingtest · Answer

actually I think andras made a little mistake...$$\int_{0}^{1} xf'(x)=xf(x)|_{0}^{1}-\int_{0}^{1} f(x)dx=1$$$$\int_{0}^{1} f(x)dx=xf(x)|_{0}^{1}-1=f(1)-1=1-1=0$$

phi · Answer

In case it isn't obvious from the posted answers, this question is about integration by parts
$$\int\limits_{}^{}u \text{ }dv=uv-\int\limits_{}^{}v \text{ }du$$
Here, let x= u  and f'(x) dx = dv

anonymous · Answer

Yeah, all I needed was for him to tell me integrate by parts. Honestly, I didn't read his actual response except that. Heh.

The steps > the answer.

anonymous · Answer

Also, I can't believe I forgot about this. I took calc just two semesters ago. >.>