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(a) For the double integral pin2 (In 2)2-y I = ef+y* dx dy. i. Sketch the...

(a) For the double integral pin2 (In 2)2-y I = ef+y* dx dy. i. Sketch the region of integration. ii. Show that I = (extu 2) (

(a) For the double integral pin2 (In 2)2-y I = ef+y* dx dy. i. Sketch the region of integration. ii. Show that I = (extu 2) (b) Using a triple integral, calculate the volume of the region in the first octant (x > 0, y > 0, z > 0), bounded by the two cylinders z2 + y2 = 4 and x² + y2 = 4.
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Solution - We have given problem, Step-I Inz Ich22_y2 ez?ty ? dx dy (1) &x= (hom2) = ly inz & y= Что, 2t x=0 1 In 2 y = In 2Jln2²_y² te x²ty 0 0 As we know 2 j y dx dy Now convert the limit by Cylinder co-ordinate x² + y² = x=8coso N2 pln2 y Y arsin

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(a) For the double integral pin2 (In 2)2-y I = ef+y* dx dy. i. Sketch the...
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