Evaluate. Show supporting work justifying your answers. Display methods, convent

Question

Evaluate. Show supporting work justifying your answers. Display methods, conventions, and standards studied in class. Integrate infinity -infinity 8 dx/X^2+9 Integrate 1 0 dx/5 squareroot (2x-1)^2 Integrate 1 0dx/7squareroot (1-x)^3 Integrate infinity 1 dx/5 squareroot(2x-1)^2 Integrate infinity -infinity dx/3 squareroot x^5 Integrate 1 0dx/5 squareroot x3 Integrate infinity 1dx/7 squareroot(2x-1)^8 Integrate 1 0 dx/7squareroot(2x-1)^8 Integrate 1 0 dx/3squareroot(1-x)7 Integrate 1 0 dx/3squarerootx^5

Explanation / Answer

f) Integration from x = 0 to 1 (x^(-3/5))dx

=from x = 0 to 1 (5/2)(x^(2/5)) (power rule)

=5/2

g)Integration from x = 1 to infinity ((2x-1)^(-8/7))dx

from x = 1 to infinity (-7/2)((2x-1)^(-1/7)) (power rule)

= 0 - (-7/2) =7/2

h)Integration from x = 0 to 1  ((2x-1)^(-8/7))dx

from x = 0 to 1  (-7/2)((2x-1)^(-1/7)) (power rule)

= (-7/2) - (7/2) = -7

i)Integration from x = 0 to 1  ((1-x)^(-7/3))dx

from x = 0 to 1  (3/4)((1-x)^(-4/3))   (power rule)

0- (3/4) = -3/4

j)Integration from x = 0 to 1  ((x)^(-5/3))dx

from x = 0 to 1  (-3/2)((x)^(-2/3)) (power rule)

-3/2

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