Question bank/JEE Main/Mathematics

y = f (x) is a function which satisfies
(i) f (0) = 0
(ii) f (x) and
(iii) f '(0) = 1
then the area bounded by the graph of y = f (x), the lines x = 0, x -
1 = 0 and y + 1 = 0, is

AeBe - 2Ce - 1De + 1

Show answer and solution▾

[IMAGE] integrating, ln f ' (x) = x + c, f ' (0) = 1 ⇒ c = 0
f ' (x) = ex
f (x) = ex + k, f (0) = 0 ⇒ k = - 1
f (x) = ex - 1

Source: Grass-G / M-01 Mathematics Paper-1.docx