Integrating powers of a linear expression: check 1
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: review variant 1
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: check 2
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: review variant 2
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: check 3
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: review variant 3
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: check 4
Difficulty: ★★☆Info
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.
Integrating powers of a linear expression: review variant 4
Difficulty: ★★☆Info
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.