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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

Determine the area bounded by the curve y = e^ -x , the X-axis and...

Determine the area bounded by the curve

y = e^{-x}

, the X-axis and the Y-axis.

Options

A $\dfrac{1}{e}$
B $1$
C $\infty$
D $e$

Correct answer

B. $1$

Step-by-step solution

The required area is bounded by the curve

y = e^{-x}

, the X-axis (

y = 0

) and the Y-axis (

x = 0

).

The area is given by the definite integral of the function from

x = 0

to

x = \infty

.

A = \int_{0}^{\infty} e^{-x} dx

A = [-e^{-x}]_{0}^{\infty}

A = -(0 - 1) = 1

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