sketch the region and evaluate the integral by changing the order of integration 22-x || (x+ y) dy dx 0 0 Find the value of a, b, c, d so that the function f(z) = (x² + axy + by²) + j(cx² + dxy + y?) is analytic.

Q: V3 (b) x V5x2 +1 dx. (Hint: be smart.)

A: We need to find the value of ∫03x35x2+1dx

Q: - 1 Then ||A|l = (-2 4 If A = Select one: а. 5 b. 6 C. 4 d. 3

A:

Q: Find the integral

A: Given integral, ∫x16+8x2dx

Q: 7. (x² + 3)² dx -2

A:

Q: Identify the method applicable and evaluate the integral using the identified method: adx 5. S -…

A:

Q: (4A)Find area bounded by y = 0, y =√x-x² using double integration.

A:

Q: use integration by parts to establish the reductionformula.

A: Integration by part formula: ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Evaluate the integral J 2x(x² + 6)¨ dx using the substitution u = x2 + 6. | 20 (a? + 6) " d.x +C

A:

Q: Evaluate the integral f 2x (x2 + 5)" dx using the substitution 16 u = x + 5. 16 2x (x² + 5)" dx = +C

A: Solve integration

Q: 3 4 Sx-3 dx x2+8x+41 (x+2)2 x2+9

A: Given,          ∫2x-3+3x+22+4x2+9+5x2+8x+41dx

Q: x² +1 dx (3x+1) 2. Evaluate

A:

Q: evaluate the integral

A:

Q: Evaluate the integral f 2x (x² +1)** dx using the substitution 14 u = x² + 1. | 20 (a² + 1)“ dx +C

A: The given integral is: I=∫2x(x2+1)14dx Substitute u=x2+1 After differentiating,…

Q: In² xdx

A:

Q: Il-Find the following integrals by suitable substitutions 1 - x. (9 + x2)) 18.dx 2- 2XVX2 + 10.dx

A:

Q: 4x2 + x – 2 dx x3 – 5x2 + 8x – 4

A:

Q: Find the solution to the following system of equations. z' + 4y = 0; y(0) = 1, and z(0) y' + z = t₁…

A:

Q: Given fe""dx = --e"3* Given [el-2)dx =--e"-2*) +c. Su;

A: Taking substirution method we have

Q: o f dx/ (x² + 4x + 5) find integral

A:

Q: x3 + 4 dx. (Be smart.) x2 +1

A: By integration, we have