16iven f(x)= 4 - IX), write the integral or integrals representing bunded by the x-axis and the portion of flx)20 a) Ss (4-1x1) dx + S (4-1x1)dx 6)5u (4-)x) dx c) Su(4-x) dx + d) A and Bonly the area Sö (4+x)dx e) A, B and only

Q: d) S */2x - ldx

A: To integrate (x⁸ ⁵√(2x³-1) dx)

Q: I) S dx/ (x² + 4x + 3) find integral

A:

Q: 1 Evaluate the integral S√I+2x f dx

A: We have definite integral  Substitute 1+2x=z2  to make integration radical free as I have done…

Q: 9) $x* 7* dx

A:

Q: Find each integral by substitution J6x(3x +1)'dx

A:

Q: 11) Find each integral by substitution a) Jóx(3x' +1)'dx 10x+1 b) ] (5x +x+8)

A: (a)∫6x3x2+18dx Let 3x2+1=u The derivative of the above equation. 6x+0=dudx6xdx=du Substitute the…

Q: Evaluate the integral of dx/sqrt(x2+4) without using the right triangle method.

A:

Q: 8. Evaluate the integral 4 + 6x dx Vx

A: In this question we have to solve the integration given. we can write , x=(x)12

Q: 35.) Simplify the following expression. 2 (2xy³2 3x³y A) B) C) D) 3y4 2x4 4y3 5x3 4y3 6x3 2y4 3x4

A: Topic = Algebra

Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

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

A:

Q: Integrate: [ z²(4x³ – 4) ªdx + C

A: We need to find out the integration.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.