Solved: "Find the exact area enclosed by the following..." - Plainmath

lenlifiauw2

Answered question

2021-11-18

Find the exact area enclosed by the following functions. (do not give decimals in the answer)
see (int1) for the functions

f (x) = x^{2}

g (x) = - 3 x + 4

Answer & Explanation

Troy Lesure

Beginner2021-11-19Added 26 answers

Upper curve is

g (x) = - 3 x + 4

Lower curve is

f (x) = x^{2}

Intersection.

x^{2} == - 3 x + 4

x^{2} + 3 x - 4 = 0

(x + 4) (x - 1) = 0

x = - 4, 1

Area

= \int_{- 4}^{1} g (x) - f (x) d x

= \int_{- 4}^{1} - 3 x + 4 - x^{2} d x

= \frac{- 3 x^{2}}{2} + 4 x - \frac{x^{3}}{3} m i d_{{- 4}}^{1}

= \frac{- 3}{2} (1 - 16) + 4 (1 - (- 4)) - \frac{1}{3} (1 - {(- 4)}^{3})

= \frac{- 3}{2} \times (- 15) + 20 - \frac{65}{3}

= \frac{45}{2} + 20 - \frac{65}{3}

= \frac{45 \times 3 + 20 \times 6 - 65 \times 2}{6}

= \frac{135 + 120 - 130}{6}

= \frac{125}{6}

Hence the area is

\frac{125}{6}

sq.units.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?