0606 · Notes & worked examples

Definite integrals and initial conditions · Short practice

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Recall

Reverse differentiation and indefinite integration — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=2 x^{4} + 21 x\), on real x.

Find the coefficient of \(\displaystyle x^5\) in a primitive.

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

Fresh review variant

Reverse differentiation and indefinite integration — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=3 x^{2} + 22 x\), on real x.

Find the coefficient of \(\displaystyle x^3\) in a primitive.

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

Method

Reverse differentiation and indefinite integration — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=3 x^{2} + 22 x\), on real x.

Find the coefficient of \(\displaystyle x^{2}\) in a primitive.

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

Fresh review variant

Reverse differentiation and indefinite integration — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=4 x^{3} + 23 x\), on real x.

Find the coefficient of \(\displaystyle x^{2}\) in a primitive.

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

For a primitive G of f satisfying \(\displaystyle G(0)=23\), 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 \(f(x)=5 \left(3 x + 4\right)^{4}\), on real x.

For a primitive G of f satisfying \(\displaystyle G(0)=24\), 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 \(f(x)=5 \left(3 x + 4\right)^{4}\), 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 \(f(x)=2 \left(x + 1\right)^{2}\), 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.

Try written exam-style problems →