Changing the order of the integration in the double integral I-08-x-42fx-ydydx leads to I-rs-pqfx-ydxdy- What is q-

I=∫_0^8∫_x/4^2f(x,y)dydx (using vertical strip) ⇒ x=0,x=8,y=x4,y=2 Afer changing the order of integration. I=∫_y=0^2∫_x=0^4yf(x,y)dxdy nbsp; nbsp; (Usi ...

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Engineering Mathematics

Change of Order

Changing the ...

Question

Changing the order of the integration in the double integral $I = \int_{0}^{8} \int_{x / 4}^{2} f (x, y) d y d x$ leads to $I = \int_{r}^{s} \int_{p}^{q} f (x, y) d x d y$ . What is $q$ ?

4 y

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16 y^{2}

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x

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8

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Solution

The correct option is A $4 y$
$I = \int_{0}^{8} \int_{x / 4}^{2} f (x, y) d y d x$ (using vertical strip)
$\Rightarrow x = 0, x = 8, y = \frac{x}{4}, y = 2$

Afer changing the order of integration.
$I = \int_{y = 0}^{2} \int_{x = 0}^{4 y} f (x, y) d x d y$ (Using Horizontal strip)
$= \int_{r}^{s} \int_{p}^{q} f (x, y) d x d y$
$\Rightarrow q = 4 y$

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Changing the order of the integration in the double integral I=∫80∫2x/4f(x,y)dydx leads to I=∫sr∫qpf(x,y)dxdy. What is q?

The correct option is A 4yI=∫80∫2x/4f(x,y)dydx (using vertical strip) ⇒x=0,x=8,y=x4,y=2 Afer changing the order of integration. I=∫2y=0∫4yx=0f(x,y)dxdy (Using Horizontal strip) =∫sr∫qpf(x,y)dxdy ⇒q=4y

Changing the order of the integration in the double integral $I = \int_{0}^{8} \int_{x / 4}^{2} f (x, y) d y d x$ leads to $I = \int_{r}^{s} \int_{p}^{q} f (x, y) d x d y$ . What is $q$ ?