0606 · Notes & worked examples

Integrating powers of a linear expression · Short practice

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Recall

Integrating a power of a linear expression — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=5 \left(x + 4\right)^{2}\), on real x.

Write a primitive as \(\displaystyle K(1x+4)^3+C\). Find K.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Integrating a power of a linear expression — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=2 \left(2 x + 1\right)^{3}\), on real x.

Write a primitive as \(\displaystyle K(2x+1)^4+C\). Find K.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Integrating a power of a linear expression — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=2 \left(2 x + 1\right)^{3}\), on real x.

For \(\displaystyle G(x)=\frac{\left(2 x + 1\right)^{4}}{4}+C\) with \(\displaystyle G(0)=17\), find C.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Integrating a power of a linear expression — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=3 \left(3 x + 2\right)^{4}\), on real x.

For \(\displaystyle G(x)=\frac{\left(3 x + 2\right)^{5}}{5}+C\) with \(\displaystyle G(0)=18\), find C.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Integrating a power of a linear expression — objective 3

Maths4U Original · Short practice

The integrand is \(f(x)=3 \left(3 x + 2\right)^{4}\), on real x.

For a primitive G of f satisfying \(\displaystyle G(0)=18\), find G(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Integrating a power of a linear expression — objective 3

Maths4U Original · Short practice

The integrand is \(f(x)=4 \left(x + 3\right)^{2}\), on real x.

For a primitive G of f satisfying \(\displaystyle G(0)=19\), find G(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Integrating a power of a linear expression — objective 4

Maths4U Original · Short practice

The integrand is \(f(x)=4 \left(x + 3\right)^{2}\), on real x.

Find the definite integral from 0 to 2.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Integrating a power of a linear expression — objective 4

Maths4U Original · Short practice

The integrand is \(f(x)=5 \left(2 x + 4\right)^{3}\), on real x.

Find the definite integral from 0 to 2.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →