Use Spherical coordinates to set up the given integral.

Q: x sec (3x) tan (3x)dx

A: ∫ xsec3xtan3xdx

Q: d. Integrate your integrals from parts c and d and show that the two integrals give the same area.

A: Given equations are: y=x2 and y=4 The integral representing area bounded by two equations with…

Q: Evaluate the integral. It may not require integration by parts. | 50² sin de

A: As the given hints i haved solved using by parts

Q: Use a double integral to find the area of the shaded region.

A: The formula for the area of a region of a polar curve, r(θ) bounded by θ=a to θ=b in the polar…

Q: Evaluate the integrals. The integrals are listed inrandom order so you need to decide which…

A: Let u and dv

Q: Determine a definite integral that represents the arc length of r = 9 sec(0), 0 < 0 < Simplify the 3…

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. sin (70) de…

A:

Q: dx (a²+x²)z 1. S- 3

A: We can a valve the given integral by using the substitution x= a tanθ.

Q: Write a triple iterated integral in cylindrical coordinates (dzdrdtheta) and solve

A:

Q: Evaluate the iterated integral: L za sin(zy)dzdyda : (Express your answer in exact form.)

A: Proceed as shown below

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9…

A: Follow the procedure given below.

Q: can you invent an exercise of double integrals with polar coordinates? to do it myself. (show the…

A:

Q: Evaluate the integrals. The integrals are listed inrandom order so you need to decide which…

A:

Q: Scot(x)dx

A:

Q: Evaluate the integrals. The integrals are listed inrandom order so you need to decide which…

A:

Q: To the polar coordinates to hich integral is transformed. when converting the integral.

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Q: cos°( VJ) y ycsc y

A:

Q: dx sin (7x)[7-cot2(7x)]

A:

Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the…

A: ∫x316-x2dx

Q: alculate the given integral. Leave your answer in exact form (do not use calculator): 6. dx 1

A:

Q: 3. S v² dv (a²-√²)1³

A:

Q: Evaluate the integral using integration by parts. Indicate the u, du, dv, and v. Full solution.

A:

Q: Evaluate the integral. If it is divergent, your answer should be o or o. 1 -dx Evaluate %3D

A:

Q: Please rewrite the integral 7² dr d0 in rectangular coordinates.

A:

Q: 1- 3 sin (x) dx. 2 cos2 (x)

A: Computer the Integral

Q: Which integral requires more steps to find? Explain. Do not integrate. | sin° x dx OR sin°x cos x dx

A:

Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

Q: 2. √a²-x² dx x2

A:

Q: Evaluate integral using integration by parts. Se- 50 sin 150 d0 Se -50 sin 150 d0 = %3D

A: Apply the integration by parts two times and simplify.

Q: How do you find the bounds for Φ to use in the triple integral when using spherical coordinates?

A: Given integral is, .Integral is evaluated over the region E.

Q: Ssin (3x)cos (3x) dx 3. Evaluate the trigonometric integral ·

A:

Q: Evaluate the integral. sec do %3D

A: According to guidelines we are supposed answer only first question if you want any particular…

Q: Set up the integral for the length of the curve: Vy - 1 from (0, 1) to (2, 5) = vy For your answer,…

A: Use formula of length of curve

Q: Calculate the iterated integral. 16 dy dx

A: The given integral is ∫116∫14xy+yxdydx Solve the integral.   Here we use the integral formula:…

Q: How do we find the area inside both cardioidsr =1+sin(0) and r = 1+cos(0)? %3D

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: /2 a) 1+sin x sin x -dx integralini hesaplayını:

A: ∫0π2sinx1+sinxdxx = π-tdx = -dtlimits x=0→t = πx = π2→t = π2∫ππ2-sin (π-t)1+sin(π-t)dt

Q: S x3 e- Bcz2 =O s as integram

A: Please check further steps for solution.

Q: Find the area enclosed by the curve r = 2 sin(0) + 3 sin(90).

A:

Q: Use a double integral in polar coordinates to find the area of the shaded region. (Give your answer…

A: Given that:

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: 2. sin t sin 2t dt

A: Our Aim is to solve the integral given below:-∫sin (t) sin (2t) dt -(i)

Q: Setup an integral to find the area of a singe leaf of r = 3sin(4*theta)

A: Definition used -               The area of a polar curve is given by -…

Q: use a double integral to find the area of the shaded region.

A: The figure is symmetrical about both axes. Therefore, initially the area of the shaded region in…

Q: dx 1+e2*

A:

Q: Use a double integral to find the area inside one leaf of r=3sin2*theta

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Q: Evaluate the integral using integration by parts. cos

A: We can solve as follows

Q: The value of the triple integral

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: 2tan(x)sec(2x)(7*ec(2x)) 1+ tan²(x) dx

A: Given integral is: I=∫-2tanxsec2x7sec2x1+tan2xdx By simplifying it: I=∫-7sec2xtan2xdx Now integrate…