The area under the curve y=2 x^3+4 x^2 between x = 2, x = 4 is: - Vidyadip

MCQ

The area under the curve $y=2 x^3+4 x^2$ between $x = 2, x = 4$ is:

✓
$192.6$
B
$198.6$
C
$88.3$
D
$172.3$

✓

Answer

Correct option: A.

$192.6$

The area under the curve is given as
$=\int\limits^4_2\ 2\text{x}^3+4\text{x}^2\text{ dx}$
$=\int\limits^4_2\ 2\text{x}^3\text{ dx}+4\text{x}^2\text{ dx}$
$=2\frac{\text{x}^4}{4}\Big|^4_2+4\frac{\text{x}^3}{3}\Big|^\frac{2}{4}_2$
$=64\times2-8+\frac{4^4}{3}-\frac{32}{3}$
$=120-\frac{224}{3}=192.6$

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