1) Calculate the following integrals: 1. S (5 +2)“ dz 2. fxe-a*/4 dx 3. S2-YE do x²– + Vx? 4. Sda x+g¤{ x²+1 dx

Q: Evaluate the integrals

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Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: -4-y Evaluate triple integral , S dz dy dx .

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Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy dx

A: Given: ∫-40∫x+42x+4siny3-3y2dydx To do: Evaluate the given double integral.

Q: S,(4y³ +-) dy y3.

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Q: Evaluate the iterated integral. (9x – 7y) dy dx 8 (9x – 7y) dy dx = -

A: We can evaluate the given integral by using the following formula

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: 14 Find the integrals using integration by parts. a. Jx(x+ 4) dx b. JVF In Vrdx c. fr'e"dx d. [ (In…

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Q: 2z •In a 5. xe¯Y dy dx dz

A: Given, ∫12∫02z∫0ln x xe-y dy dx dz

Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

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Q: (x + y) dx dy Jo Jy/2

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Q: B- Evaluate the integral 1-x (3-x-y dz dy dx /1-x²

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: 14 Find the integrals using integration by parts. b. JF In /rdx In a. fx(x + 4)°dx c. fr'e"dx d.…

A: Just multiply by 1and go ahead.

Q: QUESTION 6 Write an equivalent double integral with the order of integration reversed. In x Sx dy dx…

A: I have draw the digram and reversed the direction of limit of integration

Q: Evaluate the triple iterated integral.

A: The given integral is ∫02∫01∫-12xyz3dxdydz.

Q: Evaluate the double integral. y dy dx O - 3x

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Q: 2. Evaluate the following integrals. a) [ex.sech (e2x + 1) dx b) [sech (2x-1) dx c) Vsinh 2x…

A: Integration by substitutions

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: Consider the following two improper integrals: (1) 1 dx г — 5 -1.7 dx (2) (x –

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Q: Calculate the iterated integral. 2 (6 7e* + 3y dx dy

A: From the given problem: I=∫02∫067ex+3ydxdy So, we can also write as: I=∫02∫067ex·e3ydxdy

Q: Evaluate the double integral : (y – 8x) dæ| dy

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Q: Evaluate the double integral 2. dy dx 3/x

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Q: 10 Why is J 5 Vx-5 11 =dx an improper integral?

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Q: Evaluate the iterated integral.

A: The given integral is ∫01∫0y6x+5y3dxdy

Q: Evaluate the iterated integral 2y dy dx 2 x +1

A: on solving this we get the

Q: Evaluate the iterated integral. x³y dy dx 15

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Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

A: The given integral is ∫02∫x22ey2dy dx In original integration, the integration order is dy dx. Our…

Q: 14 Find the integrals using integration by parts. xp_ († +x)xf • - dx c. fr'e"de e flnx'de d. f (in…

A: Solution: The objective is to find the value of the given integral

Q: Calculate the iterated integral. 12 2ex + 3y dx dy

A: Consider the inner integral, name it as I1 Take the constant 2 out of the integral sign.

Q: Evaluate the iterated integral. 4 1 (3x – 5y) dy dx -1

A: We need to evaluate the value of the following iterated integral ∫14∫-113x-5ydydx

Q: 4. Calculate the following integrals: 4 3 dx 1 – x2 dz 25z2 + 1

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Q: Evaluate the iterated integral. (3x - 2y) dy dx 1 Jo

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Q: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: Evaluate the iterated integral of 2 2x . (x2 + 2y) dy dx

A: Evaluate the double integral

Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: Evaluate the iterated integral. 4 (x2 – 2y²) dx dy

A: Given problem:-

Q: Evaluate the double integral : (y – 12x) da dy 0.

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Q: Evaluate the iterated integral. (8x – 2y) dy dx

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Q: Find the integral by Integration By Parts. 2. 0 cos r0 de 3. cos t dt 4. x² sin x dx

A: Integrating By Parts Rule.

Q: Evaluate the double integral dy dx 4. 2.

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Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

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Q: Evaluate the integral. In 2 ey dx dy

A: Explanation of the answer is as follows

Q: 9. Evaluate the integrals. dx dx b. Siya Jã(1+x) 1/3

A: The integral function is ∫131dxx1+x

Q: Evaluate the iterated integral. In 5 In 3 4x+2y dy dx e 0 1 In 5 In 3 | 4x+2y dy dx = 0 1 (Type an…

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Q: Evaluate the iterated integral. 5 (бх — 10y) dy dx -1 5 (бх — 10у) dy dx%3 i

A: