Find Area Using Definite Integral: [5,10]

[rowdy3]

Use the definite integral to find the area between the x-axis and F(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval.
F(x)= 4x-32 ; [5,10]
I did
y = 0
=> 4x - 32 = 0
=> x = 8
=> graph crosses x-axis at x = 8
Also it is +ve for x > 8 and -ve for x < 8
=> required area
= - ? (x=5 to 8) (4x - 32) dx + ? (x=8 to 10) (4x - 32) dx
= - (2x^2 - 32x) ... (x=5 to 8) + (2x^2 - 32x) ... (x=8 to 10)
= - [(128 - 256) - (50 - 160)] + [(200 - 320) - (128 - 256)]
= - (-128 + 110) + (-120 + 128)
= 18 + 8
= 26. Is that right?

 

[vela]

Looks good!