(a) Find an approximation to the integral (x2 - 9x) dx using a Riemann sum with right endpoints and n = 8. Re = (b) If fis integrable on [a, b], then f(x) dx = lim f(x) Ax, where Ax =- b - a and x; = a +i Ax. Use this to evaluate (x² – 9x) dx- i= 1

Q: Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx…

A: We have to find the definite integral by using midpoint riemann sum and trapezoidal rule

Q: f (2x² + 4x + 5) dz (a) Find the Riemann sum for this integral using right endpoints and n= 3. R3…

A: Answer

Q: Assume that f is continuous and | f) dt 3 sin х — х сos x. 0, (a) Determine f(;n). (b) Find f'(x).

A:

Q: Evaluate the integral f 2x (x2 + 5)" dx using the substitution 16 u = x + 5. 16 2x (x² + 5)" dx = +C

A: Solve integration

Q: Consider the function f(x) = x(x² + 3)". (a) Use the Fundamental Theorem of Calculus to evaluate |…

A: (a) Consider the given function as fx=xx2+37

Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: Evaluate the integral f 2x (x² +1)** dx using the substitution 14 u = x² + 1. | 20 (a² + 1)“ dx +C

A: The given integral is: I=∫2x(x2+1)14dx Substitute u=x2+1 After differentiating,…

Q: Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule…

A: Integration and derivative

Q: Which integral can be approximated by a right Riemann sum where f(x) = 2x3 + 3 on the interval [2,…

A:

Q: Determine n=0 1 L th (2n + 1)! An (x) An+1(x) dx, from the relation: n tn+1 LA -1 An (x) An+1(x) dx

A: Given Information:To find:The value of .Concept used:The power series of sine function is .

Q: Q2) Evaluate the integral x* dx 0.

A: To evaluate the given integral

Q: make the ODE's inot variabke separable using a substitution. dy/dx=((1-2x-5y)^1/2 )/((2x+5y)^1/3

A:

Q: Show that cosh x> 1 + x² for all x.

A: comparison

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.