# IB Math HL – Integration

**Q**uestions and **A**nswers

### 1. Integration, Integrals – IB Mathematics HL

How can we find the following indefinite integral?

Solution

Divide by cos^2x

### 2. Integration, Integrals – IB Mathematics HL

How can we find the real number p>1 for which the following definite integral equals to 2?

Solution

So, since

### 3. Kinematics, Integration, Integrals – IB Mathematics HL

How can we find the times at which a particle comes to rest when is moving in a straight line with acceleration and with initial speed ?

Solution

We know that the acceleration

So,

Next, we find the constant by setting the initial conditions of the problem (for t=0 , v=60)

.

Therefore, the velocity function is

The particle comes to rest when

### 4. Integration, Integrals – IB Mathematics HL

How can we find the following indefinite integral?

Solution

### Evaluate a Definite Integral on the TI-84

### Indefinite Integral – Power Reducing Substitution

### Indefinite Integral – Using Trigonometric Substitution

### Integration by Parts Twice

### Integration by Parts Involving Trig Function

### Application of Definite Integration (Distance)

### Determining Area Between Two Curves – Integration Application