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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 = 3x^2 + 6x + 7 and the...

Determine the area bounded by the curve

y = 3x^2 + 6x + 7

and the X-axis between the ordinates

x = 5

and

x = 10

.

Options

A $1100$
B $1370$
C $1135$
D $1205$

Correct answer

C. $1135$

Step-by-step solution

The required area is given by the definite integral of the curve

y = 3x^2 + 6x + 7

from

x = 5

to

x = 10

.

A = \int_{5}^{10} (3x^2 + 6x + 7) dx

Integrating the function with respect to

x

:

A = \left[ x^3 + 3x^2 + 7x \right]_{5}^{10}

Substituting the upper and lower limits:

A = (10^3 + 3(10)^2 + 7(10)) - (5^3 + 3(5)^2 + 7(5))

A = (1000 + 300 + 70) - (125 + 75 + 35)

A = 1370 - 235

A = 1135

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