Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval [-2, 5] is 4 and L (8f(x)+K) dx = 34, where K is a real number. Calculate 3K.

Q: Consider the function f(x) where. 2x²-x +3. if x>2 jf x=2 if x<a f(x) = 4 4-X Is the function…

A: Solution:

Q: Evaluate integral of interval 1, 1/2 of (x-3 -8) d x

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Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: Find the open intervals on which the function f(x)=x+6*sqrt(5−x) is increasing or decreasing.

A: Given, f(x)=x+65-x

Q: Estimate the area under the graph of f(x) = √x + 4 over the interval [−4, −2] using eight…

A: fx=x+4 To find: The area under the graph fx=x+4 over the interval -4,-2 using the midpoint formula…

Q: What is the length L of the interval on which the function f(x)=x4e−x is increasing?

A: Given

Q: Determine the values of x for which f (x)=x",x >0 is increasing or decreasing.

A:

Q: f (x) = x + 2x³ – x² – 2 %3D

A: Given: Determine if the given function is continuous at every real number f(x)=x4+2x3-x2-2

Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

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Q: Find the value(s) of "c" that satisfy the conclusion of the Mean Value Theorem for the derivative of…

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Which derivative of f tells us whether the function is increasing or decreasing?What do we check to…

A: Given function ,  f(x) = ln ( x2 + 2x + 5)  Find interval of increasing and decreasing .

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.