Imagine you have two chemicals floating around in a chamber that react in equal quantities to make a product. The law of mass action tells that in this case, the rate of reaction is directly proportional to the product of concentrations of reactants. This leads to the following formula to find the time, T, taken by the chemical reaction to create a quantity q of the product (in molecules) from quantities a, b of reactants: k dx T(a) = , (a – a)(b – x)' where k is a positive constant depending on the chemicals and physical conditions. Suppose 0 < a < b. (a) Find the time taken to make a quantity q = a/2 of the product, i.e. to consume half of the a reactant. (b) Does the improper integral T(a) converge or diverge? What does this mean physically?

Q: accidently posted two questions. with this one

A:

Q: To solve the following integral, you have to make a change of variable. Select from the items, the…

A: To find the value of the integration we use the change of variable. Offer change of variable we find…

Q: What is meant by a specified integral?

A: Integration:  Integration in mathematics is the process to find the antiderivative of function. This…

Q: Evaluate the indefinite integral: ST 7xe² dx = = + C.

A:

Q: Please explain the rules applied in each step of the solution

A:

Q: sec? x dx 11. V50 – sec? x

A:

Q: 1. Use Integration by parts to solve the following integrals. Show all your work, including the…

A: Given:-             Use Integration by parts to solve the following integrals. Show all your work,…

Q: Use the definition of the definite integral (page 378) to find the exact value of the definite…

A:

Q: (b) Solve the following integrals by using substitution and exponential rule and verify the answers.…

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Do the following definite integrals. "Spax ²-lax ²-6x tadax…

A:

Q: dx Tx-1 4

A:

Q: S sec 3B tan 33 dB

A: The given integral is indefinite integral.

Q: State the limit definition of integnal. Use the definition to derivate the following definite…

A: Answer

Q: Please do not solve the integral, What does the integral mean, Is it infinite?

A:

Q: 1 Show J xd|x| = 1, by definition of RS-integral. %3D -1

A:

Q: ex (e*+2)2

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

Q: It asks for the value of the integral, and it says the answer should be 1, but I got -1. Can you…

A:

Q: Evaluate the following integrals: (1) ²²x²yzdxdydz (2) 0 Jo [²²³² (x² + y² +2²) dxdydz

A:

Q: 3 dx V16-x²

A:

Q: Using integration by parts, solve the following indefinite integral dx 5x + x2

A: The given integral is                                          ∫dx5x+x2

Q: Evaluate the following integrals. x +3 a) dx. Vx? - 4x – 5

A:

Q: If the WSS process (X(t)} is given by X(f)=10cos(100+), where pis uniformly distributed over (-s.r).…

A: The average power is given by EXt2=∫-∞∞Xt2fφϕdϕ. Since, φ us uniform so, fφϕ=12π for -π≤ϕ≤π and 0…

Q: 3 2. scc?x tanxdx

A: In this question we have to Solve the Integration.

Q: x* + 8 dx x3

A:

Q: 11 8 xr xeza S. XE 16.

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.