Area under the curveHard
Question
If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then 
xf′(x) dx is
xf′(x) dx isOptions
A.3/2
B.1
C.5/4
D.-3/4
Solution
We have f(x) dx = 
; Now, xf′(x)dx = x f′(x)dx - f(x) dx
= [x f(x)]02 - = 2f(2)- = 0 - (∵f(2) = 0) = -
f(x) dx = ; Now, xf′(x)dx = x f′(x)dx - f(x) dx= [x f(x)]02 -
= 2f(2)- = 0 - (∵f(2) = 0) = - Create a free account to view solution
View Solution FreeMore Area under the curve Questions
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides havi...Let $A_{1}$ be the bounded area enclosed by the curves $y = x^{2} + 2,x + y = 8$ and y-axis that lies in the first quadr...The whole area of the ellipse = 1 is-...Common area between the parabolas y = 2x2 and y = x2 + 4 is-...Suppose y = f(x) and y = g(x) are two functions whose graphs intersect at three points (0, 4), (2, 2) and (4, 0) with f(...