Question

Calculate the area bounded by the curve y = (−)6x2 + 24x10, the x-axis and the ordinates x = 0 and x = 4.

a. 10 unit^2
b. 104 unit^2
c. 77 unit^2
d. 134 unit^2

Answer 1

Calculate the area bounded by the curve $y = (-)6x2 + 24x + 10$ , the x-axis and the ordinates $x = 0$ and $x = 4$ .

Solution

$$S = \int_ {a} ^ {b} f (x) d x = F (b) - F (a)$$ $$\begin{array}{l} S = \int_ {0} ^ {4} (- 6 x ^ {2} + 2 4 x + 1 0) d x = = - 2 x ^ {3} + 1 2 x ^ {2} + 1 0 x \Big | _ {0} ^ {4} = \\ = - 2 * 4 ^ {3} + 1 2 * 4 ^ {2} + 1 0 * 4 - 0 = - 1 2 8 + 1 9 2 + 4 0 = 1 0 4 \\ \end{array}$$

Answer: 104 square units.