If we want to evaluate the integral 1-J x+7 1= x² + 64 dx, we use the trigonometric substitution x = becomes, in terms of 0, de and dx = The antiderivative in terms of 0 is (do not forget the absolute value) I = Finally, when we substitute back to the variable x, the antiderivative becomes Use C for the constant of integration. de and therefore the integral +C

Q: Use a trigonometric substitution to integrate the function f(x)=x√x² - 9 x². Check your work by…

A: put put x2-9=sin2t⇒2x dx=2 sin t cos t dtNow∫x (x2-9) dx=∫sin2t [sin t cos t dt]=∫sin2t. cos t .dt…

Q: 6. 1, 5, 11, 19, 29, 7. 1, 4, 10, 20, 35, 1 1 1 1 1 8. 1, | 2 3´4´5´6 3 7 9 9. 1•2 3•4 5•6´7•8 10.…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: Evaluate 11 2 By (+³+1)2 dx dy 24 by reversing the order of integration

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Q: J te √x5 + 1 dx

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Q: 7. 3. dx x + 4x - 4 8. dx

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Q: Please help. The answer is not 4.

A: Step 1: By applying the Power Rule of Integration, ∫xadx=a+11​xa+1+c ,  Step 2: To find the…

Q: [secvadx 9. sinx+cosx dx 10. cosx

A: We have to find the integration by substitution.

Q: 1 14.) Evaluate the following definite integral: √x+1 dx

A: Given integral is ∫0113x+1dx Put t=3x+1. Then dt = 3dx.  If x=0 then t=1 If x=1 then t=4 So, the…

Q: To evaluate 26 sin(x) da we can apply integration by parts x6 times. We set u = on the first…

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Q: integration for

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Q: 0 5 X 31x² - 32 do

A: Given, ∫01x31x2-325dx The given integral is solved using substitution method.