Area under the curveHard
Question
y = f(x) is a function which satisfies-
(i) f(0) = 0 (ii) f″(x) = 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 -
(i) f(0) = 0 (ii) f″(x) = 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 -
Options
A.e
B.e - 2
C.e - 1
D.e + 1
Solution
l nf′(x) = x + c⇒ f′(x) = kex
⇒ f ′(x) = ex {f ′(0) = 1 ⇒ k = 1}
⇒ f (x) = ex + λ
⇒ f (x) = ex - 1 {f (0) = 0 ⇒ λ = - 1}
A =
(ex -1 + 1) dx = e -1
⇒ f ′(x) = ex {f ′(0) = 1 ⇒ k = 1}
⇒ f (x) = ex + λ
⇒ f (x) = ex - 1 {f (0) = 0 ⇒ λ = - 1}
A =
(ex -1 + 1) dx = e -1Create a free account to view solution
View Solution FreeMore Area under the curve Questions
The area of the region$R = \left\{ (x,y):xy \leq 8,1 \leq y \leq x^{2},x \geq 0 \right\}$ is...The area of the region$A = \left\{ (x,y):4x^{2} + y^{2} \leq 8 \right.\ $ and $\left. \ y^{2} \leq 4x \right\}$ is :...The area of the region between the curves y = and y = bounded by the lines x = 0 and x = is...The area enclosed between the curves y = loge (x + e), x = loge and the x-axis is...If area bounded by the curve y2 = 4 ax and y = mx is a2/3, then the value of m is -...