Use known area formulas to evaluate the integrals in Exercises 23–28 ždr, dx, b > 0 23. 24. 4x dx, b > 0 3t dt, 0 < a < b 25. 2s ds, 0 < a < b 26. 27. f(x) = V4 – x? 28. f(x) = 3x + V1 – x² on a. [-2, 2], b. [0, 2] on a. [-1,0], b. [-1, 1]

Q: Sx(x – 7)12 dx Integrate

A: Hence,  ∫x(x-7)12dx=(x-7)1414+7(x-7)1313+C          Where C is an integral constant .

Q: Compute the integration da dy 1+メ+ye

A: I use polar conversion method to solve this double integral

Q: Exercise 8. let C be any closed simple curve and f(z)=lz+il. Then the integral of f(2) over C is 0.…

A: Given C, any closed curve.  And f(z)=|z+ i|

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

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

Q: -2Y dy y°e

A: The given integral is: I=∫y3 e-2y dy

Q: س1/ حل التكامل التالي dx (x + 2) Vx2 + 4x+ 3

A:

Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

A:

Q: Define the Trigonometric functions?

A: Trigonometric functions: A function of an angle that is expressed as the ratio of the two sides of a…

Q: The integraing factor of (4xy+3y² – x)dx + x(x+2y)dy3D0 is (A x-2 B 2x-2 2x-1 D D x2

A: Since, the given differential equation is not exact . To make it exact we find integrating factor ,…

Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

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Q: Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y=-x-2. SS₂² dA R

A:

Q: b) g(x) = S,* In(2r + 1)dr

A:

Q: Find all local extrema for 4 f(x, y): * - 4xy + y.

A:

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

A:

Q: 1-CAL182 y =Vx+4 29- y=x-2 SVx+4dx + [(Jx +4- (x – 2))dx → a = ?,6 = 2,c = ?,d = ? area = A) a- 4,…

A: Break the function into interval and find value of limit for each interval.

Q: Solve da d. t 4824 dx2 , * & hat 8 -utort) = 4(8, () = 0, (X,0) = 4X= ( 1 ) X ²

A: Given partial differential equation∂u∂t=4∂2u∂x2Using forward difference for the first order…

Q: What is the af dy of f(x, y) = tan (x²y³ + 2xy)?

A: Topic- Partial differentiationf(x,y)=tan(x2y3+2xy)we know that,ddx(tanx)=sec2xddxxn=nxn-1 We are…

Q: 9.) S(5t + 2t2 - 5t - 50)dt

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: In integrating the function fin Srdr using integration by parts, what would you choose for your de?

A:

Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: Integrate: x dx (xt1)(x*+2)

A: Given data: The given integral is I=∫x2(x+1)(x2+1)dx. The given integral can be written as,…

Q: Integrate: ia 3A/3 A. +C 4 В. 1 C. 32/3 D. 31/3 +C

A:

Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: 3- Verify the properties (HINT Use integration by parts) F[ux] = iF[u] F[uxx] = -²F[u]

A: