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Mars2501 [29]
1 year ago
7

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), an

d the x-axis.
Mathematics
1 answer:
Dvinal [7]1 year ago
4 0
First find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =
[\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216= 72+0=72

the area under the curve bounded by the lines and the x axis is 72 square units
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