Question

By using the properties of definite integrals, evaluate the integral

Answer 1

so break the integration from -5to -2 + -2 to 5

taking first case -5 to -2
x^2/2+2x= (-2)^2/2+(-2)×2-(-5)^2/2-2×(-5)
=4/2-4-25/2+10=-21/2+6=-9/2 reverse the integraion we will get +9/2


taking next case from -2 to 5
x^2/2+2x= 25/2+10-(-2)^2/2-2×(-2)
=25/2+10-4/2+4=21/2+14=49/2

now adding two cases

49/2+9/2=58/2=29 ans

hope it helps..

it is more easy using graph...