Use calculus to find the area A of the triangle with the given vertices. (0, 7), (3, −4), (4, 2)

Answer 1

(0,7), (3,-4), (4,2)

heron's formula

s=semi-perimeter= about 11.9

Area= sqr[s(s-sqr130)(s-sqr41)(s-sq37)

or use the law of cosines to find the angle between 2 sides= 132.978 degrees= A between b and c

b and c = sqr41 and sqr37

then use the formula Area = (1/2)bcSinA = about .5sin132.978sqr(41x37)=14.248

Use calculus, but divide the x values into 5 numbers for limits of evaluation for the integrals

0, 21/11, 3, 11/3, and 4, otherwise the integral will cancel out negative areas below the x axis, rather than add them Whatever you get, it should be about 14.248

whoever came up with this problem may be a tad sadistic. if they really wanted you to use calculus, when there are easier ways to do it. Looking at the graph, the triangle's area looks about 14. Just doing geometry with estimates. But do the calculus, if you have the time, it gets tediously time consuming with lots of room for mistakes along the way

Answer 2