Maths4U Original · Short practice

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

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

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

Maths4U Original · Short practice

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

Find the coefficient of \(\displaystyle e^{1x}\) in a primitive.

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

Maths4U Original · Short practice

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

For \(G(x)=e^{3 x}+C\) 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.

Maths4U Original · Short practice

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

For \(G(x)=4 e^{x}+C\) with \(\displaystyle G(0)=19\), find C.

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

Maths4U Original · Short practice

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

For a primitive G of f satisfying \(\displaystyle G(0)=19\), find \(\displaystyle G(\frac{\ln (3)}{1})\).

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

Maths4U Original · Short practice

The integrand is \(f(x)=5 e^{2 x}\), on real x.

For a primitive G of f satisfying \(\displaystyle G(0)=20\), find \(\displaystyle G(\frac{\ln (3)}{2})\).

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

Maths4U Original · Short practice

The integrand is \(f(x)=5 e^{2 x}\), on real x.

Find the integral from 0 to \(\displaystyle \frac{\ln 4}{2}\).

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

Maths4U Original · Short practice

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

Find the integral from 0 to \(\displaystyle \frac{\ln 4}{3}\).

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