Sketch the region enclosed by the given curves and calculate its area. y=4-x^2 ,y=0 The answer is 32/3. But how do I get t

Question

Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0

The answer is 32/3. But how do I get to that answer?

in progress 0
Farah 3 years 2021-09-02T11:48:02+00:00 1 Answers 84 views 0

Answers ( )

  1. Sigrid
    0
    2021-09-02T11:49:16+00:00
    Reply

    Answer:

    Step-by-step explanation:

    1.) we need to find the bounds of integration which is just the points of intersection

    here is it (-2,0) and (2,0)

    which means we will integrate from -2 to 2

    next, we take the upper equation and subtract that from the lower one

    kind of confusing but it would look like (sketch it out if you’re not sure)

    (4-x²)-0= 4-x²

    then we can integrate

    \int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )