Question

定积分简单计算例题

几道简单定积分计算题,
(1) ∫0到5 4x dx （2）∫0到5 (x^2-2x)dx (3)1到2（根号下x-1）dx （4）-1到3 （3x^2-2x+1）dx

Answer 1

∫(0,5)4xdx
=2x²|(0,5)
=50-0
=50
∫(0,5)(x²-2x)dx
=(1/3x³-x²)|(0,5)
=(125/3-25)-(0-0)
=50/3
∫(1,2)√x-1dx
=2/3(x-1)^(3/2)|(1,2)
=2/3(2-1)^(3/2)-2/3(1-1)^3/2
=2/3
∫(-1,3)(3x²-2x+1)dx
=x³-x²+x|(-1.3)
=(27-9+3)-(-1-1-1)
=21+3
=24