Question

. Evaluate the fulówing intógrals: tle ioibwai erdz c-boundary ofe square with sides; z ±2、y= ±2 circle |s| 1 b+ cos@ b.

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SOLUTION 0 (x2+2)2 We apply the changee x-V2 tanu -»u- tan -1 (仮 lhen (x2+2)2 ((V2 tan u)2+2)2 2tan (u (2tan2(u) +2)2 2ta㎡(11

tan-1 4 Finally (x2 + 2)2 4 V2 =_| lim l tan- - tan -- Sin2tan _ i 42 24 2 2 4 $2

2TT ele b+Cose If we apply the change 1-1θ-> du idθ du dθ i0 lu b + Cos0 2u dv If we use that v (2v + 2b) - b we have2 r5(2v + 2b) - b 2 11) (20 + 2b) (1 (2v+2b) We can saythat -n27-5dv and 2-b Solving for : dw We use the change w v2 + 2bv +If we apply the changes tvb+Vb2-1 -> dt - dv and q-v b dq - dv we getLn(t) - Ln(C2 Now, we apply

Finally we have 2Tt ίθ 0THESE QUESTIONS ARE NOT TOPICS OF PHYSICS. THEY ARE TOPICS OF MATH ADVANCED.

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