y = f(x) is a function which satisfies : f(0) = 0 f"(x) = f'(x) and 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 :

Definite Integration

Grade 12

Question:

y = f(x) is a function which satisfies : <ol start="1" style="list-style-type: lower-roman;"> <li>f(0) = 0</li> <li>f"(x) = f'(x) and</li> <li>f'(0) = 1</li> </ol> then the area bounded by the graph of y = f(x), the lines x = 0, x - 1 = 0 and y + 1 = 0, is :

e

e - 1

e + 1

e - 2

Step-by-Step Solution

Key Concept: Solve the linear differential equation with initial conditions to find the function f(x), then calculate the area using the definite integral of the difference between f(x) and the lower boundary y = -1.

e - 1

Correct Answer: B

Question:

Step-by-Step Solution

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