Integration by Parts: Solve Integral of (1-x)

[matematikuvol]

Homework Statement

Solve integral
\int^{1}_0(1-x)\frac{d}{dx}\frac{\sin Cx}{C}dx

Homework Equations

\int udv=uv-\int vdu

The Attempt at a Solution

u=1-x

dv=\frac{d}{dx}\frac{\sin Cx}{C}dx

What is v?

How to integrate

\frac{d}{dx}\frac{\sin Cx}{C}dx?

 

[Mark44]

Homework Statement

Solve integral
\int^{1}_0(1-x)\frac{d}{dx}\frac{\sin Cx}{C}dx

Homework Equations

\int udv=uv-\int vdu

The Attempt at a Solution

u=1-x

dv=\frac{d}{dx}\frac{\sin Cx}{C}dx

What is v?

How to integrate

\frac{d}{dx}\frac{\sin Cx}{C}dx?

Is C a constant?

Why not just differentiate sin(Cx)/C?

 

[dynamicsolo]

How to integrate

\frac{d}{dx}\frac{\sin Cx}{C}dx?

What is the anti-derivative of a derivative?

 

[HallsofIvy]

Fundamental Theorem of Calculus!