Question

Find the area of the region to the nearest hundredth of a square unit from the curve f(x) = x3 + 3x2 - 10x to the x-axis over the interval [-5, 2].

a.101.75 square units
b.93.00 square units
c.104 square units

Answer 1

\[required area=\int\limits_{-5}^{2}f \left( x \right)dx\]\[=\int\limits_{-5}^{2}\left( x ^{3}+3x ^{2}-10x\right)dx=\left[ \frac{ x ^{4} }{ 4 }+\frac{ 3x ^{3} }{ 3 } -\frac{ 10x ^{2 } }{ 2 }\right]( -5 to 2)\]

Answer 2

so where do i go from here?

Answer 3

you plug in 2 for x and then plug in -5 for x and subtract the two answers

Answer 4

\[=\frac{ 1 }{ 4 }\left\{ \left( 2 \right)^{4}-\left( -5 \right)^{4} \right\}+2^{3}-\left( -5 \right) ^{3}-5\left\{2^{2} -\left( -5 \right)^{2}\right\}\]
solve it.