Convert the integral 1/2 √9 - x² LE**** √ 18-x² - y2 dz dy dx into an integral in spherical coordinates and evaluate it. 3 × 1 < ) / ( 1²1 ) - (IT) ]x )√₂ 1³ cos (0) sin(0) + rz dp dp de = 18 (√2-1)
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- How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the sphere x2 + y2 + z2 = 25, the cylinder x2 + y2 = 9, and the xy-plane, using spherical coordinates? Solving these integrals by hand is way too difficult, so I just need to find the limits of integration in terms of ρ, φ, and θ.If the integral∫4−4∫√16−y2−√16−y2∫√16−x2−y2−√16−x2−y2(x2+y2+z2)dzdxdywas converted into an integral in spherical coordinates, we would get:Evaluate double integral - 3 to 3, 0 to underoot (9-x^2) sin(x^2 +y^2) dydx
- Prove that Coth-1x = 1/2 In (x + 1 / x - 1), x > 1 Hence or otherwise show that (i) Coth-1( 1 + 2tan2u ) = -In sinu (ii) the integral of e2coth-1 dx = x + 2In(x - 1) + kconsider limaçon r = 2 + 3 cos θ and the circler = 2 cos θ in one polar plane. - Set up the definite integral that solves the area of the regioninside the circle and outside the loop. SET UP, DO NOT SOLVE VALUE!! tyEvaluate the integrals ∫cos (1 - ln y)/y dy