examday

/TMUA

A student approximates the integral $\displaystyle\int_a^b\sin^2 x\,\dd x$ using the trapezium rule with 4 strips. The resulting approximation is an overestimate.

Which of the following is/are necessarily true?

• I If the student approximates $\displaystyle\int_{-b}^{-a}\sin^2 x\,\dd x$ in the same way, the result will be an overestimate.
• II If the student approximates $\displaystyle\int_a^b\cos^2 x\,\dd x$ in the same way, the result will be an underestimate.