1) (D* t 180* + 81) y =0

Q: 8. dx :) x² +9 0.

A:

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: (1 –2²)dz

A:

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: 5. Use the substitution method to evaluate So 3x²+2 x3 + 2x +37 dx.

A: Topic = Integration

Q: (b) (x*y2,1/3(xy) -1/3 X + 0, y # 0

A: We will simplify the expressions by writing the exponents with equating the bases.

Q: 6) Evaluate 0.8 1 0 dx 4x² +4

A:

Q: Determine the length of x = ¹³ (y − 1)³/² between 1 ≤ y ≤ 4.

A: Thank you 😊

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: d) S 2xe* dx

A:

Q: a

A: Here we have to evaluate I=∫xex1+exdx ...........................(1)

Q: et Evaluate dx using an appropriate substitution. 1+ e2x a

A:

Q: In x dx = n a, (a>0) 2a 23. Show that

A: Definite integration is the area of a region that is enclosed by the integrand. The function must be…