Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 + 12y – 36y2 dy 3 -1 108 бу — 1 бу — 1 7 (1+ 6y – 36y²) ² + 2 72 + C x y · - 12 36

Q: Evaluate the integral fa* (2* – 11)"dz, dx, by making the appropriate substitution: u = 11). 24 dx =…

A: ∫x3x4-1124dxSubstitute u=x4-11du=4x3dxdu4=x3dx

Q: Complete integral of the equation z = px+ qy – 2pq is, (a) z = ax+ by – Vab (b) z = ax+by + Vab (c)…

A: Clairaut's form is given by z = px+qy+f(p,q) Its complete integral is given by z = ax+by+f(a,b)

Q: Q#01: Find the complete integral of x²p? + y²q? – 4 = 0 using Charpit's method.

A: To find the complete integral of using Charpit's method.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the const 6 + 12y – 36y2 dy 3 + ( 6y…

A: Given ∫y-36y2+12y+6dy⇒6∫y-6y2+2y+1 dy⇒∫y-6y2+2y+1dy , write y as 16-1122-12y and…

Q: Evaluate by reversing the order of integration of S. xe y dydx хе у b) c) 0 d) None of these 1/2

A: The given integral is ∫0∞∫0x xe-x2ydy dx. We need to evaluate the integral by changing the order of…

Q: b) Change the order of integration in the following double integrals: 1. ff(x,y) dxdy. 2. ²-y²…

A: We will change the order of the given integrations

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

A:

Q: Solve the triple integral I| (x² + y² + z²)7/2 dV where B is the unit ball B O 2n 2л О Зл 5 o 7n 5 O…

A:

Q: If 9. 10 f(2)dæ = /: | F(2)dx - / f(x)dæ, f(x)dx + %3| 3 9, what are the bounds of integration for…

A:

Q: dx = V9x2 + 1 Use the appropriate substitution to evaluate the following integrals: ... /9x² + 1 +C…

A:

Q: Evaluate the integral: r+∞ 1 dv v²+2v-3

A: We will find the integral.

Q: If 10 12 f(2)dz = [f(2)a | f(z)dx- - f(=)dz, f(r)dx + 10 what are the bounds of integration for the…

A:

Q: (a) Change the order of integration and hence evaluate fo M*(ry)dydx.

A:

Q: 17 dx x2 Evaluate the improper integral: а) О-17 b) Odiverges c) O17 d) 034 e) Ov17

A: Given,

Q: In approximation of f(x)dx by Romberg Integration, if R, =0.25 and Ry =0.2525, then R= O None of…

A:

Q: In approximation of f(x)dx by Romberg Integration, if R,=0.25 and R21 =0.2525, then R22= O None of…

A: Romberg Integration method is used to improve the approximate results obtained by finite difference…

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

A: The integration of the integral is 1/[x^(1/3)+x^(1/2)].

Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

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

Q: e2z Q5- The value of the integral . Sc Where C is Z =3 (Z+1)4

A:

Q: We'll now apply the integration by parts procedure to the new integral e70 cos(80) d0, letting U =…

A: The given integral,∫e7θ cos(8θ) dθ

Q: 2x f²f²² (x² + 2y³) dy dx. Write the iterated integral in the previous item using the order dx dy.

A:

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ +1| + C dx…

A: Given

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx…

A: To evaluate: ∫dxx3+x Let I = ∫dxx3+x Assuming x=u6⇒dx = 6u5du

Q: Reduce to first order and solve. (1 - x2 )y" - 2xy' + 2y = 0, y1 = x. Use : fp dx = In [1/(1- x²)] ,…

A:

Q: e the method of u-substitution to evaluate the given integrals. 4t dt 2 – 8t2

A:

Q: The Particular Integral for (D2 + 5D + 6)y = e3z O None O Yp 30 elz O Yp O Yp =

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Given: p(x,y)=(3/100)xy^2 Find the probability of x>y. Express this as an iterated integral, or as…

A: Given: Px,y=3100xy2 1.  dxdy Px>y=∫∫Px,y dxdy Therefore, Px>y=∫∫3100xy2dxdy=3100∫y2∫x…

Q: 3z+4 dr Use the appropriate substitution to evaluate the following integrals: e %3D O e3a+4 + C ©…

A:

Q: 1. Evaluate the following integrals |(1 - 2)Vī dx 13 (ii) (2 – t4)d' (iii) 24 – 523 + 6x² – 18 da a3…

A:

Q: In evaluating z(4– 2)šdx,if we use the substitution that u = 4– 2, then what will be the resulting…

A:

Q: Q1 (a) Compute the multiple integrals of (i) V4-22 xy dxdydz (11) S, (8 – x² – y²)dA, where R =…

A: In this question we will use basic of calculus i.e concept of multiple integration. We will simply…

Q: Reverse the order of integration and then evaluate the integral. Lx*ey dxdy O el6 . – 68 O 4el6 – 68…

A:

Q: Evaluate the integral i.) 2 S² S₂y ez dxdy हैं,

A:

Q: Apply the appropriate integration techniques to evaluate 9x? dx S- а. b. fxsin dr. 2 c. f(2x – 8)°dx…

A:

Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

Q: Evaluate the integrals below. -4 x²+6 а. 1 Vx t/7 b. sin(t) dt It/3 c. Sx2Vx3 + 2 dx

A: a.=∫14x2+6xdx=∫14(x2-12+6x-12)dx=∫14(x32+6x-12)dxintegrating=[x32+132+1+6x-12+1-12+1]14…

Q: In x)2 To evaluate aX, apply integration by parts twice. For the second application of integration…

A:

Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A:

Q: If 10 14 [ f(2)da = / f(2)dz | f(2)dæ + f(z)dæ – | f(t)dt, 10 what are the bounds of integration for…

A:

Q: (c) Evaluate the following iterated integrals by changing the coordinate system: 16-x2 Vx² + y² + z²…

A: According to the spherical coordinates , x=rsinθcosϕy=r sinθsinϕz= r cosθJ=r2 sinθx2+y2+z2=r2 To…

Q: 2. Evaluate the following integrals (a) / 20° 2x + 3х — 2 dx (b) /: 3x2 + Vx dx (c) / t (Vi – 3t) dt

A:

Q: 1 dx. 10. Evaluate the improper integral m 64 + z²

A:

Q: Use integration by parts to find the integral. (Use C for the constant of integration.

A: It is required to solve the integration by parts:

Q: If 11 16 F(=)dz = | f(2)dz + f(2)dz – f(=)dr, 11 what are the bounds of integration for the first…

A:

Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 7/3 "s(:) dz 3 -2 2p (2)f…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.