Question

The interval [a, b] such that the value of $\int _ { a } ^ { b } \left( 2 + x - x ^ { 2 } \right) d x$ is maximum, is

• A. [-1, 2]
• B. [-2, 1]
• C. -2,-1
• D. [1,2]

Answer 1

Answer: (A)

$-1, 2$

Answer 2

The integral$\int _ { a } ^ { b } \left( 2 + x - x ^ { 2 } \right) d x$will give us the algebraic sum of areas bounded by the parabola y = 2 + x − x², x-axis and the lines x = a and x = b. The expression 2 + x − x² is non-negative in [−1, 2]. Thus [a, b] should be [-1, 2].