Calculus Question

Question

Let F(x)=∫ sin(t^3) dt from 0 to x for 0≤x≤2. 

Use the trapezoidal rule with four equal subdivisions of the closed interval [0,1] to approximate F(1). Round to three decimal places.

Please show all work.

Answer 1

F(1) = ∫_{(0 to 1)} sin(t³)dt Δt = (b-a)/n = (1-0)/4 = 0.25

≈ [(b-a) / (2n)] (sin0 + 2sin(0.25)³ + 2sin(0.5)³ + 2sin(0.75)³ + sin1)

= (0.125)(0 + 2sin(0.25)³ + 2sin(0.5)³ + 2sin(0.75)³ + sin1)

Evaluate. Note: Calculator must be in Radian mode.