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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


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


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


Integrate 5-3e to the power of4x which is divided by e to the power of x. 4x x trying to write it would be : 5-3e divided by e


Integrate with respect to x (3+4x) to the power -1


Dy/dx = x³ - √x + 3 - secxtanx Find y = I got the following answer:y = x4/4 - 2x (3/2)/3 + 3x - secx Is it correct????

Partial Fractions

Find the integral of a polynomial fraction. See attached file for full problem description.