Integration by Parts: Solve y(1+y^2)^1/2 dy

Thread starter Song
Start date Nov 10, 2006
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Integration Integration by parts parts

In summary, integration by parts is a calculus method used to find the integral of a product of two functions. It is typically used when other integration techniques are not applicable and when the integrand is a product of two functions. The formula for integration by parts is ∫ u dv = u v - ∫ v du, and it involves identifying u and dv, finding their derivatives and antiderivatives, and solving for the integral. Some tips for effectively using integration by parts include choosing u to be the more complicated function, using tabular integration, and simplifying the integrand before applying the formula.

Nov 10, 2006

Song

integral y(1+y^2)^1/2 dy

can someone help me with this?

Thanks.

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Nov 10, 2006

Song

trigonometirc sub.

Nov 10, 2006

Bernie Hunt

Wouldn't this solve easier with u substituion?
u = 1+y^2
du = 2y dy

Solution is 1/3(1+y^2)^3/2

If you want integration by parts, multiply it out and make u to be y so that du is 1.

By trig you'll need to substitute tan because the problem is + Y^2.

Bernie

FAQ: Integration by Parts: Solve y(1+y^2)^1/2 dy

1. What is integration by parts?

Integration by parts is a method used in calculus to find the integral of a product of two functions. It involves breaking down the original integral into two parts and using the product rule for differentiation to solve for one of the parts.

2. How do I know when to use integration by parts?

Integration by parts is typically used when the integral of a function cannot be easily determined using other integration techniques, such as substitution or trigonometric identities. It is also used when the integrand is a product of two functions.

3. What is the formula for integration by parts?

The formula for integration by parts is: ∫ u dv = u v - ∫ v du, where u is the first function, dv is the differential of the second function, v is the antiderivative of dv, and du is the differential of u.

4. How do I solve the given equation using integration by parts?

To solve the given equation, first identify u and dv. In this case, u = (1+y^2)^1/2 and dv = dy. Then, find the derivatives of u and the antiderivative of dv. Plug these values into the integration by parts formula and solve for the integral.

5. Are there any tips for using integration by parts?

Some tips for using integration by parts effectively include choosing u to be the more complicated function, using tabular integration for repetitive integrals, and simplifying the integrand as much as possible before using the integration by parts formula.