What is the area under the curve f(x) = 3 $x ^ { 2 }$ + 2x + 1 from x = - $\frac { 3 } { 2 }$ to x = - $\frac { 1 } { 2 }$ ?
A) $\frac { 9 } { 4 }$
B) $\frac { 51 } { 4 }$
C) $\frac { 15 } { 4 }$
D) - $\frac { 15 } { 4 }$
E) none of these

Question

Quizplus · Accepted Answer

The area under the curve is given by the integral of the function over the given interval. So, we have:$$\int_{-3/2}^{-1/2} (3x^2 + 2x + 1) dx$$$$= \left [ x^3 + x^2 + x \right ]_{-3/2}^{-1/2}$$$$= \left [ (-1/2)^3 + (-1/2)^2 + (-1/2) \right ] - \left [ (-3/2)^3 + (-3/2)^2 + (-3/2) \right ]$$$$= \left [ -1/8 + 1/4 - 1/2 \right ] - \left [ -27/8 + 9/4 - 3/2 \right ]$$$$= \left [ -9/8 \right ] - \left [ -15/8 \right ]$$$$= \frac{9}{4}$$Therefore, the area under the curve is 9/4.

What Is the Area Under the Curve F(x) = 3 x2x ^ { 2 }x2

What Is the Area Under the Curve F(x) = 3 $x ^ { 2 }$