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  1. find the average value of the function f(x) = x2 over the interval [1,4].
  2. find the area under the curve y= 4 – x2 over the interval [0,2].
  3. evaluate the indefinite integral: 2x cube root (x2 + 1) dx.
  4. evaluate the indefinite integral: (lnx)3/ x dx.
  5. Evaluate the definite integral: x(x2 + 1)3 dx with lower bound 0 and upper bound 2.
  6. Evaluate the definite integral: sin5(2x) cos(2x) dx with lower bound 0 and upper bound pi/8
  7. evaluate the definite integral: x square root (x2 + 1) dx with lower bound 0 and upper bound 1.
  8. Evaluate the definite integral: xe (-xsquared/2) dx with lower bound 0 and upper bound square root 2.
  9. Find the area of the region under the graph of y= 1/ (1+ x2) over the interval [0,1]
 
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I know that the answer is already shown, but I don’t understand it and would like somebody to show me steps by steps.

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5. Find the average value of the function f (x) = tan2 x from x = 0 to x =%. Then find all values c that satisfy the conditions of Mean Value Theorem for Integrals. 4 Average value = — —l71′ c=tan"[ i—ljmsms71′

 
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Find the area under the curve y=4e^ (2x) over 0≤x≤8.

please explain each step

The graph of the function is given by; Now to find the area we have to integrate the function y=4ex over with 0 as the lower limit and 8 as the upper limit (2x) with respect to Now plugging in the…

 
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,……. statics and probablity… MAT – 201 SLU – ………

Find the area oi the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standarddeviation of 15‘ Click to View page 1 of the table. Click to View page 2 at the table. T5 115 The area of the shaded region is . {Round to four decimal places as needed.) pp

 
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A) compound amount after 5 years

B) Intrest earned

Find the compound amount for the deposit and the amount of interest earned. $6200 at 3% compounded quarterly for 5 years The compound amount after 5 years is $|:|.(Do not round until the final answer. Then round to the nearest cent as needed.) The amount of interest earned is $|:|.(Do not round until the final answer. Then round to the nearest cent as needed.)

 
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Find the coefficient of the squared term in the simplified form for the second derivative, f “(x) for f(x) = (x2 + 4x + 3)(4×3 − 6×2 + 8x + 1). Use the hyphen symbol, -, for negative values. (Show working)

 
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Need help with these integral questions please show your step by step process because I want to get the methods down.

4. Find the center of mass of the thin plate covering the region bounded by theparabola y = x2 and the line y = x.

 
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Please could you kindly help me out here with this questions.

Find the capacitor voltage in the network shown in Figure 134.2 if the switch closes at t= 0.Assume zero initial conditions. Also find the time constant: rise time: and settling time for thecapacitor voltage. Plot the step response for the problem ab ovel using MATLAB. From your plots: find the timeconstant: rise time= and settling time.

 
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…………………………………………………………………

2. Find the derivative of the following functions using the product rule, quotient rule, orchain rule. You do not need to simplify the result.(a) (1 point) y = cos (2′)(b) (1 point) f (x) = tan ‘(4x)(c) (1 point) g(x) = e 2: In(1-3x)(d) (1 point) h(x) = log,(1+2x)(e) (1 point) y = xcos(x)

 
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Find the derivative of each of the following functions, first by using the product rule, then by multiplying each function out and finding the derivative of the higher-order polynomial. Post both solutions along with explanations of the intermediate steps that demonstrate your understanding of the derivative.

1. (4x + 6)(9x-5)

2. 4x^2(3x^3 -2x^2 +5x)

3. (3x^2 -x + 1)(7-x^6)

4. (h^3 -5)(3h^2 -5h – 4)

 
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