0 votes 0 votes For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these Calculus isi2017-mma engineering-mathematics calculus integration + – Tesla! asked Apr 24, 2018 edited May 11, 2019 by akash.dinkar12 Tesla! 1.2k views answer comment Share Follow See 1 comment See all 1 1 comment reply ankitgupta.1729 commented Apr 24, 2018 reply Follow Share Integral gives Area under curve. So, here ,f(x) = 7x−x2−10 = - (x2 - 7x +10) = -[(x-5)(x-2)] So, f(x) is a downward parabola because coefficient of x2 is negative and it cuts X-axis at points x = 2,5 So,here in the question 'a' should be 2 and 'b' should be 5 because a<b Now, when we solve this integral , answer will be 9/2 4 votes 4 votes Please log in or register to add a comment.