Question

Consider the following. $$\int x\sqrt{x - 20} \, dx$$ The integral can be evaluated using integration by parts with the following choice of u. $$u = x$$ Determine du, dv, and v. $$du = (1) \, dx$$ $$dv = (\sqrt{x-20}) \, dx$$ $$v = \frac{2}{3}(x-20)^{(\frac{3}{2})}$$ Evaluate the integral. (Remember the constant of integration.) $$\int x\sqrt{x - 20} \, dx = $$

Name: consider the following int xsqrtx 20 dx the integral can be evaluated using integration by parts with the following choice of u u x determine du dv and v du 1 dx dv sqrtx 20 dx v frac23x 20f 81687
Uploaded: 2024-10-09T12:56:06-08:00
Duration: 2 min 6 s
Channel: Gregory Higby
Description: consider the following int xsqrtx 20 dx the integral can be evaluated using integration by parts with the following choice of u u x determine du dv and v du 1 dx dv sqrtx 20 dx v frac23x 20f 81687

          Consider the following.
$$\int x\sqrt{x - 20} \, dx$$
The integral can be evaluated using integration by parts with the following choice of u.
$$u = x$$
Determine du, dv, and v.
$$du = (1) \, dx$$
$$dv = (\sqrt{x-20}) \, dx$$
$$v = \frac{2}{3}(x-20)^{(\frac{3}{2})}$$
Evaluate the integral. (Remember the constant of integration.)
$$\int x\sqrt{x - 20} \, dx = $$

$consider the following int xsqrtx 20 dx the integral can be evaluated using integration by parts with the following choice of u u x determine du dv and v du 1 dx dv sqrtx 20 dx v frac23x 20f 81687$

Added by Timothy P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

10/09/2024

Step 1

We are given $dv = \sqrt{x-20} \, dx$, so $v = \frac{2}{3}(x-20)^{3/2}$. Using integration by parts, we have $$\int u \, dv = uv - \int v \, du$$ $$\int x\sqrt{x-20} \, dx = x \cdot \frac{2}{3}(x-20)^{3/2} - \int \frac{2}{3}(x-20)^{3/2} \, dx$$ $$= Show more…

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Consider the following. $$\int x\sqrt{x - 20} \, dx$$ The integral can be evaluated using integration by parts with the following choice of u. $$u = x$$ Determine du, dv, and v. $$du = (1) \, dx$$ $$dv = (\sqrt{x-20}) \, dx$$ $$v = \frac{2}{3}(x-20)^{(\frac{3}{2})}$$ Evaluate the integral. (Remember the constant of integration.) $$\int x\sqrt{x - 20} \, dx = $$