Example 1: Evaluate the integral: ₁²²=238+1² 2r-3 - 3x + 1 dx.

Q: Evaluate the integral: S/2 sin(4t - u) du dt

A: The integration of the double integral is Sin(4t-u), u from 0 to t, t from pi/2 to pi.

Q: show that V(x, y) = x 'f (2x+y) is the genera Solution of : du 2X x av ах 1 ду

A: First, we find ∂v/∂x and ∂v/∂y  and substitute them in the given equation, if it satisfies the…

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

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Q: Evaluate: £²₁² [(x²-²²] du dt 2 y²)²₁ x+y

A: Given, ∫-13∫02(x2-y2)2(x+y)dudt

Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: Evaluate the following √ (2²2 + + 6x − 1)²(x + 3)dx (x²+6x-1)-5 + C 2 (x²+6x-1)-5 3 +C (x²+6x - 1)5…

A: We have to solve given integration.

Q: Find the first and second derivative of the function. 3 G(r) = √r + √r G'(r) G"(r) || =

A: Find the derivative

Q: Given a second order differential equation dx X = e³t dt where t = 0, x = 2. 3t Using Laplace…

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: Given : Let I be a proper ideal of the commutative ring R with identity. Then I is a _______ if and…

Q: 4. Evaluate the double integral: Y SZ (Hint: Change the order of integration to dy dx.) dx dy. +1…

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Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

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Q: -In Evaluate the integral: ²²ste du ds dt

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Q: Evaluate the following * [: 2x(4x² – 3)³dx (4x²-3)6 +C 24 O (4x² - 3)-6 24 +C (4x²-3)6 24 O " (4x² -…

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Q: Find the area of the region bounded by the curves 1 y = (x+8)2 y = 4 and the x-axis using vertical…

A: Explanation of the answer is as follows

Q: 1. Find the cofactor of 6 in matrix D 9 8 4 2 -9 3 4 D= -3 2 3 3 2 968 7 6 (8 9

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Q: 3. √ √1 + x² dx

A:

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: We have to find the volume of solid generated by revolving the region bounded by 2y = e-(x^2) , the…

Q: late the integral: ſ³ ſt²eªu du di dt

A:

Q: Find the general solutions for these differential equations: a. 2y²dx + (x²y - 2xy)dy = 0 b. y' =…

A: Use differential equation concept

Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

Q: Find the volume of the solid generated by revolving 1 the region bounded by y = e¯x², the x-axis and…

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Q: f(x, y) = x² - y² + 10x +12y - 64 −x² −

A: To determine the extrema if any for the given function.fx, y=-x2-y2+10x+12y-64

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: 1. Find the angle between two vectors a and b with magnitudes √3 and 2, respectively having a b =…

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Q: Solve the given differential equation. All solutions should be found. dyx³ 8y dx X NOTE: Use c for…

A: As we know that; The standard form of 1st linear order differential equation is: dydx+Pxy=Qx So, the…

Q: PARKING THIS BLOCK 2AM TO 5AM 2 HOUR PARKING THIS BLOCK 9AM 6PM EXCEPT SUNDAYS 15 MINUTE PARKING…

A: Ques (a) According to the third sign (at the bottom), the parking time is between 8 AM to 5 PM. So…

Q: Choose 1 answer: A 13 klo ㅠ 4t2 + 16 sec4 (t) dt

A: Please refer to the image below

Q: 2 (x² - y²) ² Evaluate: ³₁² L 21 x+y du dt

A: We have to find value of given double integration.

Q: Find the area of the region bounded by the curves 1 (+6)² = 4 and the x-axis using vertical strip

A: using vertical strip we have  Area=∫-∞∞∫1x+624dydx

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis and…

A: Given problem is :

Q: Evaluate: xy² dx dy

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Q: 3 S S t² etu du dt

A:

Q: Solve the general solution of the following Linear differential equation: y' = x - 2xy

A: Let us consider a differential equation of the form, dydx+P(x)y=Q(x) So its integrating factor is…

Q: strip.

A: y-axis using the horizontal strip ,  y = 0 , x = 4/0+1 , x=4  so y-axis at x=4 and y= 0. Area of…

Q: (x + 2)" Q4. Find the convergence interval and radius of the series : Σ (-1)**² n=l n

A: We need to find interval and radius of convergence.

Q: Evaluate: ₁³₂₁(4x²y — z³) dz dy dx -2

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral. ƒ ƒ6(x³ - y³)²dA = □ (Type an exact answer.) R

A: ∫-11∫016x3-y32dA

Q: In Evaluate the integral: Sto st² sin s teu du ds dt

A: The given integral is: I=∫12∫tt2∫0lnsteududsdt   The Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: Solve the differential equation. x dy dx = y + x³ + 3x² -2 x

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Q: Evaluate: ³₂(4x²y - 2³) dz dy dx

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Q: integral: 2² sin (-) dt du Evaluate the integral:

A: use substitution method and integration of parts for solving the integral

Q: Function f is graphed. -4 -3 -2 A Y 4 3 2 t 1 1 4 2 3 -1+ -2- -3- -4 Find f (2) da. Give an exact…

A: We can find the given integral by using the application of the integral.

Q: -3 (x² - y²)²] Evaluate: ₁²² x+y du dt

A: Given

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: he table of integrals to evaluate the integral. (Use C for the constant of integration.) sin (20) J…

A: The solution is given below.

Q: و و ۹۷۶) (0) لا او A 2 1 - X Jx (x+2 - 4

A: This is a problem related to differentiation. Based on the general formula and concept we will…

Q: 2 t √3u Evaluate the integral: №³4 524 4²2 ds du dt s²+u²

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Q: Find the particular solution of the DE y11 + 24y = 0 subject to the initial conditions y(0) = 2 and…

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Q: Solve the given differential equation. All solutions should be found. dy 3x²-2y-y³ 13 dx 2x + 3xy²…

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