S x3 e- Bcz2 =O s as integram

Q: 5. Sx³e2* dx

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Q: S x²ye" dxdy

A: The integral is given as , ∫23∫02x2yeydxdy Change order of integration.

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. IL-…

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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: 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 integral by interpreting it in terms of area. integral -3 to 0(1+(9-x^2)^1/2)dx

A: Let us assume y=1+(9-x2)12 y-1=(9-x2)12(y-1)2=9-x2x2+(y-1)2=9This is an equation of a circle with…

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

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Q: (x²–16)3/2 -dx x3

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Q: Use a double integral to find the area of the cardioid r = 5 – 5 cos 6 -

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A: Integration by parts:∫uvdx = 4∫vdx - ∫[ddx(u)∫ vdx]dx

Q: Use a double integral to find the area of the region. The region inside the circle (x − 3)2 + y2 =…

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Q: Show that arctan(Tx) – arctan(x) -dx In T. by first expressing the integral as an iterated integral.

A: To show

Q: 2 B. Evaluate | (2- x) dx by interpreting the integral in terms of area. -1

A: Topic = Integration

Q: Find the complete integral xp+3yq D2 (z - xq). 2 2 the

A: Consider the given equation: The objective is to find the complete integral of given equation.

Q: Evaluate the integral by first reversing the order of integr. NOTE: Enter the exact answer. dy dx 2x

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Q: ind the integral using integration by parts. Do not use a table of ntegrals. ze -dz

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Q: a) Evaluate the indefinite integrals using Tabular Integration by parts. i) ſx³ V2x + 1dx

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Q: Evaluate the integral using integration by parts where possible. r In(8r)dx

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Q: The area of the region outside the curve r-2+2sin0 and inside the curve r-6sin0 is given by which…

A: given:- r=2+2sin∅ r=6sin∅

Q: (4x-1)dx (2x+1)Z 3

A: ∫(4x-1)dx2x+13/2 Let  2x+1=y ⇒ 2x=y-1⇒4x=2y-2⇒4x-1=2y-3

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. 489x хе dx…

A: ∫xe489x dxBy using integration by partsu=x, v=e489x

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -9x In(2)…

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

A: We have to use a double integral to find the area of the shaded region.

Q: Use a double integral to find the area of the shaded region. -2 π/2 6 2 2 -4 -6 r=3+3 cose 2 4 0

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

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Q: In 2 sinh?xdx - In 2

A: Given problem:-

Q: S In 5x dx

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Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

A: ∫(2-x)2x dxApply linearity:=-∫(x-2)*2x dxIntegrate by parts ∫fg'=fg-∫f'gf=x-2 and g'=2xf'=1 and…

Q: Evaluate the integrals using integration by parts. ∫(r2 + r + 1)er dr

A: We have to integrate using integration by parts: ∫r2+r+1erdr When two function is in product then we…

Q: Use a double integral to find the area of the shaded region. 7/2 20 r= 9+9 cos e 10 - 10 -5 5 10 15…

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Q: 6. Evaluate the iterated integral by first reversing the order of integration. Do not use technology…

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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: Evaluate the integral using integration by parts. cot -1(5y)dy

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Q: Evaluate the integrals using integration by parts. ∫p4e-p dp

A: ∫p4e-p dp

Q: 3. Evaluate the integral using integration by parts: |p° ln p dp

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Q: | x(2x – 1)"da

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Q: Use a double integral to find the area of the shaded region. 1/2 10 r= 5+5 cos e -5 5 10 -10

A: The integral of a function is with respect to two different variables, so if f is a function of two…

Q: Use a double integral to find the area of the shaded region. n/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5…

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Q: Use the properties of integrals and ex dx = e3. (Sex - 1) dx. - e to evaluate %3D

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Q: -1Vx X. dx Vx cos

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Q: Identify u and dv for finding the integral using integration by parts. (Do not evaluate the…

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Q: 2-V1-x dx by interpreting the integral in terms of area. -

A: ∫-112-1-x2 dx On simplification, we get ∫-112-1-x2 dx=∫-112 dx-∫-111-x2 dx   →1 Now consider, ∫-112…

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: we have to evaluate the integral: ∫01x3-3x2dx using the definition of integral, ∫abf(x)dx=limn→∞∆x…

Q: Evaluate the integrals using integration by parts. ∫(x2 - 2x + 1)e2x dx

A: To evaluate ∫x2-2x+1e2xdx

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: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

A: We need to compute the integral using integration by parts with the indicated choices of u and dv.

Q: Evaluate the integral using integration by parts. cos

A: We can solve as follows

Q: 5. Ssin' x dx.

A: I am attaching image so that you understand each and every step.