- #1

Song

- 47

- 0

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

can someone help me with this?

Thanks.

can someone help me with this?

Thanks.

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- Thread starter Song
- Start date

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.

- #1

Song

- 47

- 0

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

can someone help me with this?

Thanks.

can someone help me with this?

Thanks.

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- #2

Song

- 47

- 0

trigonometirc sub.

- #3

Bernie Hunt

- 19

- 0

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

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.

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.

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.

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.

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.

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