All High School Math Resources
Example Questions
Example Question #21 : Calculus Ii — Integrals
Evaluate:
Example Question #22 : Calculus Ii — Integrals
Find
This is most easily solved by recognizing that .
Example Question #1 : Integrals
Remember the fundamental theorem of calculus!
Since our , we can't use the power rule. Instead we end up with:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #1 : Finding Definite Integrals
Remember the fundamental theorem of calculus!
Since our , we can use the reverse power rule to find the indefinite integral or anti-derivative of our function:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #43 : Comparing Relative Magnitudes Of Functions And Their Rates Of Change
Remember the fundamental theorem of calculus!
As it turns out, since our , the power rule really doesn't help us. has a special anti derivative: .
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #44 : Comparing Relative Magnitudes Of Functions And Their Rates Of Change
Remember the fundamental theorem of calculus!
As it turns out, since our , the power rule really doesn't help us. is the only function that is it's OWN anti-derivative. That means we're still going to be working with .
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Because is so small in comparison to the value we got for , our answer will end up being
Example Question #31 : Calculus Ii — Integrals
Remember the fundamental theorem of calculus!
Since our , we can use the power rule for all of the terms involved to find our anti-derivative:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #2 : Finding Definite Integrals
Remember the fundamental theorem of calculus!
Since our , we can't use the power rule. We have to break up the quotient into separate parts:
.
The integral of 1 should be no problem, but the other half is a bit more tricky:
is really the same as . Since , .
Therefore:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #5 : Integrals
Remember the fundamental theorem of calculus!
Since our , we can use the power rule, if we turn it into an exponent:
This means that:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve:
Example Question #6 : Integrals
Remember the fundamental theorem of calculus!
Since our , we can't use the power rule, as it has a special antiderivative:
Remember to include the for any anti-derivative or integral taken!
Now we can plug that equation into our FToC equation:
Notice that the c's cancel out. Plug in the given values for a and b and solve: