Question

6. Evaluate the integrals: a) ?_D(x²-y²)dA where D={(x,y) | -1?x?1, -2?y?2} b) ?_D[12-(1/4)x-(1/8)y]dA where D={(x,y) | 0?x?8, 0?y?16}

          6. Evaluate the integrals:

a) ?_D(x²-y²)dA where D={(x,y) | -1?x?1, -2?y?2}

b) ?_D[12-(1/4)x-(1/8)y]dA where D={(x,y) | 0?x?8, 0?y?16}

Added by Daniela A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/15/2023

Step 1

Since -1 < x < 1 and -2 < y < 2, we can write the double integral as: $$\int_{-1}^1 \int_{-2}^2 (x^2 - y^2) dy dx$$ Now, we can evaluate the inner integral with respect to y: $$\int_{-1}^1 \left[ xy^2 - \frac{1}{3}y^3 \right]_{-2}^2 dx$$ Plugging in the limits Show more…

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