Maths4U Original · Short practice

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

For \(G(x)=2 e^{2 x}+C\) with \(\displaystyle G(0)=23\), 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 \(f(x)=5 e^{3 x}\), on real x.

For \(\displaystyle G(x)=\frac{5 e^{3 x}}{3}+C\) with \(\displaystyle G(0)=24\), 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 \(f(x)=24 \sin{\left(3 x \right)} + 5 \cos{\left(3 x \right)}\), on real x.

For \(\displaystyle G(x)=\frac{5 \sin{\left(3 x \right)}}{3} - 8 \cos{\left(3 x \right)}+C\) with \(\displaystyle G(0)=25\), 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 \(f(x)=25 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\), on real x.

For \(G(x)=2 \sin{\left(x \right)} - 25 \cos{\left(x \right)}+C\) with \(\displaystyle G(0)=26\), 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 \(\displaystyle f(x)=\frac{2}{x + 1}\), on \(x>-1\).

Find the x-coordinate of the pole.

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 \(\displaystyle f(x)=\frac{5}{x + 4}\), on \(x>-4\).

Find the x-coordinate of the pole.

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