2) Prove that: a) dx' dx- b) F) = dF %3D Ldx dx c) [x,p²]= 2h?d/dx

Q: Evaluate 3 | ((2 – 1)32, (3 + t)2, 1)dx. 3/2 3/2 -3

A:

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

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: Which is NOT included in evaluating the integral? (Use partial fraction decomposition method.) 4 2x…

A:

Q: Compute: 1+2 dx

A:

Q: Use implicit differentiation to find dy/dx and dy/dx2. x²+y2%D5, at the point (2, 1) dv d2v =D2B 3D5…

A:

Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

A:

Q: Integrate: a+2– +2x²-1 dx

A:

Q: x2+1 - dx x4-x²+1

A:

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: sinh x 20. 1x1-3 A) 2. B)-2. D) 0.

A:

Q: 1) 3 )dx

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

Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: 3x + 2 dæ, Hint: Remember that 4 = 4 + . = +. A+B 4. b) Integrate %3D

A:

Q: dy Differentiate implicitly to find dx 5 3 5 ху 2 2 Xy + 6x¯ = 8y +7 %3D

A: Given equation is x3y5+6x52=8y52+7. Compute the implicit derivative.…

Q: dy Differentiate implicitly to find dx exy 2x+9y+3

A:

Q: Differentiate, hcx) = In (x-Vr

A:

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

A: