Evaluate the definite integral of the following function.

Question

Evaluate the definite integral of the following function that has points through (0,2), (7,4), (8,-4) and then a continued straight line.

Which of the following is the definite integral

∫12

0

dt.

a)2

b)38

c)34

d)0

Answer 1

Here is the parabola that passes through those 3 points:

y = Ax^2+Bx+C

(0,2) ---> C = 2 ---> y = Ax^2+Bx+2

(7,4) ---> 49A + 7B + 2 = 4

49A + 7B = 2

(8,-4) ---> 64A + 8B +2 = -4

64A + 8B = -6

32A + 4B = -3

49A + 7B = 2

32A + 4b = -3

Elimination: -4 * eq1 and 7*eq2

-196A + -28B = -8

224A + 28B = -21

28A = -29

A = -29/28

49 ( -29/28) + 7B = 2

(7/4)(-29) + 7B = 2

-203/4 + 7B = 2

7B = 2 + 203/4 = 8/4+203/4 = 211/4

B = 211/28

y = (-29/28)x^2 + (211/28)x + 2

integrate that function