Question

Calculus 3 Assessment #6 Page 3 of 4 3. Express $\int_{-1}^{1} \int_{0}^{\sqrt{1-x^2}} \int_{0}^{x^2+y^2} xz\sqrt{x^2+y^2} \,dz \,dy \,dx$ in cylindrical coordinates. Do not evaluate the integral.

          Calculus 3
Assessment #6
Page 3 of 4
3. Express
$\int_{-1}^{1} \int_{0}^{\sqrt{1-x^2}} \int_{0}^{x^2+y^2} xz\sqrt{x^2+y^2} \,dz \,dy \,dx$
in cylindrical coordinates. Do not evaluate the integral.

Calculus 3
Assessment #6
Page 3 of 4
3. Express
∫-1^1∫0^√(1-x^2)∫0^x^2+y^2 xz√(x^2+y^2) dz dy dx
in cylindrical coordinates. Do not evaluate the integral.

Added by Heidi D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert H M

Step 1

In cylindrical coordinates, x is represented as rcosθ, y is represented as rsinθ, and z remains the same. So, we can rewrite the integral as ∫((rcosθ)^2 + (rsinθ)^2)dzdydx. Simplifying the expression inside the integral, we get ∫(r^2cos^2θ + Show more…

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