Maths4U Original · Short practice

The integrand is \(f(x)=18 \sin{\left(3 x \right)} + 3 \cos{\left(3 x \right)}\), on real x.

Find the coefficient of sin(3x) 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 \(f(x)=19 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\), on real x.

Find the coefficient of sin(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 \(f(x)=19 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\), on real x.

Find the coefficient of cos(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 \(f(x)=20 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)}\), on real x.

Find the coefficient of cos(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 \(f(x)=20 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)}\), on real x.

For \(\displaystyle G(x)=\frac{5 \sin{\left(2 x \right)}}{2} - 10 \cos{\left(2 x \right)}+C\) 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 \(f(x)=21 \sin{\left(3 x \right)} + 2 \cos{\left(3 x \right)}\), on real x.

For \(\displaystyle G(x)=\frac{2 \sin{\left(3 x \right)}}{3} - 7 \cos{\left(3 x \right)}+C\) 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 \(f(x)=21 \sin{\left(3 x \right)} + 2 \cos{\left(3 x \right)}\), on real x.

Find the integral from 0 to \(\displaystyle \frac{\pi }{6}\).

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.

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

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