For the curve on the interval

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

For the curve

r=\theta^{2}

on the interval

0\le\theta\le\tfrac{\pi}{2}

, the integrand

g(\theta)=\bigl(r\bigr)^{2}=\theta^{4}

satisfies

\left|g''(\theta)\right|\le 30

throughout the interval. Determine the least even number

n

of equal subintervals that guarantees the absolute error of a trapezoidal approximation of the area is no greater than

0.05