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!