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Popular >

integral from 0 to 3 of 1/((x-1)^2)

Solution

\int_{0}^{3} \frac{1}{( x - 1 ) ^{2}} d x

Solution

diverges

Solution steps

\int_{0}^{3} \frac{1}{( x - 1 ) ^{2}} d x

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{1} \frac{1}{( x - 1 ) ^{2}} d x + \int_{1}^{3} \frac{1}{( x - 1 ) ^{2}} d x

\int_{0}^{1} \frac{1}{( x - 1 ) ^{2}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

Popular Examples

area y=6x-x^2,y=2x area

y = 6 x - x^{2}, y = 2 x

limit as x approaches 0 of 1/x ln(1-6x)

x \to 0 lim (\frac{1}{x} ln (1 - 6 x))

(dy)/(dx)=2.5-(5y)/(2x+100)

\frac{d y}{d x} = 2.5 - \frac{5 y}{2 x + 100}

integral of (9-x^2)^2

\int (9 - x^{2})^{2} d x

integral of (2x)/(x^2+2x+2)

\int \frac{2 x}{x ^{2} + 2 x + 2} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of 1/((x-1)^2) ?
The integral from 0 to 3 of 1/((x-1)^2) is diverges