Maths4U Original · Short practice

The integrand is \(f(x)=5 x^{3} + 20 x\), on real x.

Find the coefficient of \(\displaystyle x^4\) 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 \(f(x)=2 x^{4} + 21 x\), 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.

Maths4U Original · Short practice

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

For \(\displaystyle G(x)=\frac{2 e^{3 x}}{3}+C\) with \(\displaystyle G(0)=21\), 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 \(f(x)=3 e^{x}\), on real x.

For \(G(x)=3 e^{x}+C\) with \(\displaystyle G(0)=22\), 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 \(f(x)=22 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\), on real x.

For \(G(x)=3 \sin{\left(x \right)} - 22 \cos{\left(x \right)}+C\) 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 \(f(x)=23 \sin{\left(2 x \right)} + 4 \cos{\left(2 x \right)}\), on real x.

For \(\displaystyle G(x)=2 \sin{\left(2 x \right)} - \frac{23 \cos{\left(2 x \right)}}{2}+C\) 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 \(\displaystyle f(x)=\frac{4}{2 x + 3}\), on \(\displaystyle x>- \frac{3}{2}\).

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 \(\displaystyle f(x)=\frac{5}{3 x + 4}\), on \(\displaystyle x>- \frac{4}{3}\).

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.