Calculus Examples

Evaluate the Integral integral from -2 to -1 of 8y^3+10/(y^3) with respect to y
Step 1
Split the single integral into multiple integrals.
Step 2
Since is constant with respect to , move out of the integral.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Combine and .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
Apply basic rules of exponents.
Tap for more steps...
Step 6.1
Move out of the denominator by raising it to the power.
Step 6.2
Multiply the exponents in .
Tap for more steps...
Step 6.2.1
Apply the power rule and multiply exponents, .
Step 6.2.2
Multiply by .
Step 7
By the Power Rule, the integral of with respect to is .
Step 8
Simplify the answer.
Tap for more steps...
Step 8.1
Simplify.
Tap for more steps...
Step 8.1.1
Combine and .
Step 8.1.2
Move to the denominator using the negative exponent rule .
Step 8.2
Substitute and simplify.
Tap for more steps...
Step 8.2.1
Evaluate at and at .
Step 8.2.2
Evaluate at and at .
Step 8.2.3
Simplify.
Tap for more steps...
Step 8.2.3.1
Raise to the power of .
Step 8.2.3.2
Raise to the power of .
Step 8.2.3.3
Cancel the common factor of and .
Tap for more steps...
Step 8.2.3.3.1
Factor out of .
Step 8.2.3.3.2
Cancel the common factors.
Tap for more steps...
Step 8.2.3.3.2.1
Factor out of .
Step 8.2.3.3.2.2
Cancel the common factor.
Step 8.2.3.3.2.3
Rewrite the expression.
Step 8.2.3.3.2.4
Divide by .
Step 8.2.3.4
Multiply by .
Step 8.2.3.5
To write as a fraction with a common denominator, multiply by .
Step 8.2.3.6
Combine and .
Step 8.2.3.7
Combine the numerators over the common denominator.
Step 8.2.3.8
Simplify the numerator.
Tap for more steps...
Step 8.2.3.8.1
Multiply by .
Step 8.2.3.8.2
Subtract from .
Step 8.2.3.9
Move the negative in front of the fraction.
Step 8.2.3.10
Multiply by .
Step 8.2.3.11
Combine and .
Step 8.2.3.12
Multiply by .
Step 8.2.3.13
Cancel the common factor of and .
Tap for more steps...
Step 8.2.3.13.1
Factor out of .
Step 8.2.3.13.2
Cancel the common factors.
Tap for more steps...
Step 8.2.3.13.2.1
Factor out of .
Step 8.2.3.13.2.2
Cancel the common factor.
Step 8.2.3.13.2.3
Rewrite the expression.
Step 8.2.3.13.2.4
Divide by .
Step 8.2.3.14
Raise to the power of .
Step 8.2.3.15
Multiply by .
Step 8.2.3.16
Raise to the power of .
Step 8.2.3.17
Multiply by .
Step 8.2.3.18
To write as a fraction with a common denominator, multiply by .
Step 8.2.3.19
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Step 8.2.3.19.1
Multiply by .
Step 8.2.3.19.2
Multiply by .
Step 8.2.3.20
Combine the numerators over the common denominator.
Step 8.2.3.21
Add and .
Step 8.2.3.22
Move the negative in front of the fraction.
Step 8.2.3.23
Multiply by .
Step 8.2.3.24
Combine and .
Step 8.2.3.25
Multiply by .
Step 8.2.3.26
Cancel the common factor of and .
Tap for more steps...
Step 8.2.3.26.1
Factor out of .
Step 8.2.3.26.2
Cancel the common factors.
Tap for more steps...
Step 8.2.3.26.2.1
Factor out of .
Step 8.2.3.26.2.2
Cancel the common factor.
Step 8.2.3.26.2.3
Rewrite the expression.
Step 8.2.3.27
Move the negative in front of the fraction.
Step 8.2.3.28
To write as a fraction with a common denominator, multiply by .
Step 8.2.3.29
Combine and .
Step 8.2.3.30
Combine the numerators over the common denominator.
Step 8.2.3.31
Simplify the numerator.
Tap for more steps...
Step 8.2.3.31.1
Multiply by .
Step 8.2.3.31.2
Subtract from .
Step 8.2.3.32
Move the negative in front of the fraction.
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Step 10