Integral of sine
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
∫₀ᵇ sin(kx) dx = (1 − cos(kb))/k
Problem
Evaluate ∫ from 0 to 1 of sin(1x) dx. Give your answer to 3 decimal places.
Working
- 1Antiderivative of sin(1x) is −cos(1x)/1.
- 2F(b) − F(0) = [−cos(1·1)/1] − [−cos(0)/1].
- 3= (1 − cos(1))/1 = 0.4597.