Definite integrals and initial conditions: check 1
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: review variant 1
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: check 2
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: review variant 2
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: check 3
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: review variant 3
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: check 4
Difficulty: ★★☆Info
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.
Definite integrals and initial conditions: review variant 4
Difficulty: ★★☆Info
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.