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Integrals

Multiple integration

Please see the attached file for the full problem description. --- 1. Transform the given integral in Cartesian coordinates to one in polar coordinates and evaluate the polar integral. : refer to integral 5. 2. Determine the values of the given integrals, where W is the region bounded by the two spheres x^2 + y^2 +

Evaluate the Definite Integrals

∫(pi/2 to 0) sin^4(x) dx -- do not use reduction forumulas use 1-cos2u/2=sin^2x ∫3x^3/sqrt(8-x^2) dx Integrate, integration

Evaluate the Integrals (4 Problems)

Evaluate each of the following integrals: 1. ∫0-->2 6/(5x+2) dx 2. ∫1-->3 e^(-0.4t) dt 3..... 4.... Please see the attached file for the fully formatted problems. Integrate, Integration

Triple integral

F(x,y,z)=y ; W is the region bounded by the plane x+y+z=2, the cylinder x^2 + z^2 = 1, and y=0. Integrate the given function over the indicated region W.

Integral

I have a function (see attached). I need to integrate it over m from - infinity to infinity, h from - infinity to infinity. I need to apply a technique such that the integral takes a simple form, easy for integration. The main problem here as you can see is product of terms in the denominator. ---

Integration : Trigonometric Integrals and Integrate by Substitution

Evalaute the integral 1) ∫ (sin^3 (x)) (cos^2 (x)) dx 2) ∫ ( sin^4 (x)) (cos^5 (x)) dx 3) ∫ ( sin^6 (x)) (cos^3 (x)) dx 4) ∫ ( sin^3 (mx)) dx 5) ∫ (from 0 to pi/2 on top) (cos^2 (theta)) dtheta 6) ∫ (from 0 to pi/2 on top) (sin^2 (2theta)) dtheta 7) ∫ (from 0 to pi on top) (sin

Integration by Substitution

Please and explain and solve the following: 13. Find the indefinite integral and check the result by differentiation. Integral: x^2(x^3 - 1)^4 dx Answer: (x^3 - 1)^5/15 + C 130. Find the indefinite integral in two ways. Explain any difference in the forms of the answers. Integral: sin x cos x dx

Double integral

Please see the attached file. Please show me the detailed process.

Area between two curves

I am not sure how to solve this. Please show all steps. F(x)=ln2x G(x)=lnx Limits: a=1 and b=5

Integration

Please show all steps to solve: Domain: 1≤t≤ e^π∕4 ∫4dt∕t(1+ln²t)

Inverse trig integration

The question asks if both of these integrations can be correct and why/why not? a) ∫dx / √1 - x² = -∫-dx/ √1-x² = -cos‾¹x + C b) ∫dx / √1 - x² = ∫-du/√(1 - (-u)²) x = -u dx= -du = ∫-du/√1- u² = cos‾¹u + C

Evaluate the integral

What is the solution? please show each step ∫ dy / (sin‾¹y)√(1­ - y²)

Evaluate the integral

How do you solve this integral in the domain shown? Please show each step. domain: ½ ≤ t ≤ 1 ∫ 6dt ∕ √(3 + 4t - 4t²)

Evaluate integral

What is the solution? Evaluate the integral: ∫dx ∕(x+3)√((x+3)² -­ 25)

Multiple Integrals, Vector Fields, Hemispheres and Divergence Theorem

B10. (a) State the Divergence Theorem, being careful to explain any notation you use and any conditions that must apply. The vector field B is given by B = Rcos θ(cos θR - sin θ ^θ ) in spherical polar coordinates (R; θ; φ). This field exists in a region which includes the hemisphere x2 + y2 + z2

Integration

Evaluate e to the power of 3x minus 4 divided by e to the power of x between the ordinate limits -2 and -3.