A student approximates the integral $\int _ { a } ^ { b } \sin ^ { 2 } x \mathrm {~d} x$ 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 $\int _ { - b } ^ { - a } \sin ^ { 2 } x \mathrm {~d} x$ in the same way, the result will be an overestimate. II If the student approximates $\int _ { a } ^ { b } \cos ^ { 2 } x \mathrm {~d} x$ in the same way, the result will be an underestimate.
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A student approximates the integral $\int _ { a } ^ { b } \sin ^ { 2 } x \mathrm {~d} x$ 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 $\int _ { - b } ^ { - a } \sin ^ { 2 } x \mathrm {~d} x$ in the same way, the result will be an overestimate.
II If the student approximates $\int _ { a } ^ { b } \cos ^ { 2 } x \mathrm {~d} x$ in the same way, the result will be an underestimate.