dx 1. S (2-3x)2 2. S V2x + 1 dx

Q: An elementary reaction is generally expressed as: dC, = -kC," %3D dt

A: Given, dCAdt=-kCAn now solve this integral dCA=-kCAndtCA-ndCA=-kdtCA-n+1-n+1=-kt+c at t=0…

Q: Solve the following Integral Equation: x(0)= 3 =-t +

A: Given ∂x∂t=-t+∫0txtdt with x0=3 We will solve the differential equation using Laplace transform

Q: 0 -2 ex+1 dx 7- ex+1

A: Given query is to find the value of the integral.

Q: 4 sin x dx (1+ cos x)2

A:

Q: 2 3 3t dt - 3 -2

A:

Q: Solve the definite integral

A:

Q: π/2 π/3 esec 2 x (sec 2x)(tan 2.x)dx

A:

Q: a Ső 8 ea - e X a dx

A: ∫0aexa-e-xadx=∫0aexadx-∫0ae-xadx=ae-1-a1-1e=ea+-2e+1ea

Q: (d) (e) (f) [ ₁² V. [ (sec²(x) — csc²(4x)) da. x² √x³+3 dx ** π/4 sin(4x) dx.

A: Detailed solutions is given below.

Q: y3 dy |(1– 2y*)$

A:

Q: TT sinx sin 2x dx 2 cos x

A: Given the definite integral ∫0π4sinx sin2x2cosxdx. The objective is to evaluate the integral.…

Q: 2r dr (1 – r)7

A:

Q: (a) So x²e*dx %3D (b) S a²2"dx = «0) f{(In(z))*dz = |

A:

Q: f(t) = 8 – 15 | "sin5r f(t-t) dt

A:

Q: 10x

A:

Q: L(3x+e")dx Jo

A: