a) What is the total area between the Area = 7 graph of f(x) in the figure and the x-axis, between x = 0 f (x) and x = 5? 3 The total area is 5 p) What is f (x) dx? Area = 6 %3D 5 f(x) dx

Q: 1. Use a suitable substitution to evaluate , (G) dx. Give you answer correct to at least 2 decimal…

A: Substitution is done for the function whose derivative is present in the numerator.

Q: 2. A hemisphere of raduus 12 nches and base up is full of water that runs out through an orifice of…

A:

Q: 2 Estimate the minimum number of subintervals to approximate the value of| (4x² + 4) dx with an…

A: We will solve both these parts using basics of numerical analysis.

Q: ne value of fe*d by dividing the range of integration qual parts using Simpson's rule is aces)…

A: Introduction: The formula of Simpson 13rd rule for n equal intervals is given by,…

Q: snip

A: Solution: Area=∫-40-xdx Let t=-x dtdx=-1 dt=-dx =∫-40-t dt =-23t32|-40 Area=0+23(4)32 =23(4)32…

Q: Graph of the function y = cos 2x What is the area of the region bounded by the x = 15°, x = 45°…

A:

Q: ind the area of the region that is enclosed between the curves x = yand x = y - 6 integrating with…

A:

Q: 3. Consider the graph of y = ln (x) + 1. Calculate the area enclosed by the curve y= ln (x) +1 and…

A: The region is bounded by y=ln(x)+1 and the y-axis between the lines y=1 and y=2

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 2…

A:

Q: Consider the mid-point rule for approximating a) Derive the erTor term b) Derive composite mid-point…

A: Consider the mid-point rule on the interval [a, b] for approximating

Q: The area of an indicator diagram taken off a four-cylinder, single-acting, four-stroke, internal…

A:

Q: 1. The region bounded by the graph of y = 2x and the x-axis over the interval [-3, 3] consists of…

A: It is given that the region of the graph y=2x is bounded by x-axis over an interval [-3,3]. It forms…

Q: 2. a) Given (x+1)dx, graph and lightly shade the appropriate region. -1 b) Approximate area: Draw…

A: Left end Riemann Sum:

Q: 1. Sketch the graphs. f(x) = x2 and g(x) = 3x - x2 %3D %3D 2. Locate the interval [a, b] by finding…

A: y=x2 to graph the function we need a few points x y=x2 -2 y=-22=4 -1 y=-12=1 0 y=02=0 1…

Q: Find the area bounded by the graphs of the indicated equations Compute answers to three decimal…

A:

Q: problem in the photo attached

A: definite integration.

Q: Approximate the positive value of the constant a such that the area enclosed by y = cosh ax, y = 0,…

A:

Q: 6. (a)Estimate the area under the graph of f(r) = 1 + r² from r = -1 to 1 = 2 using three rectangles…

A: Reimann sum

Q: phical evidence and other area facts to find: 3 2 1 (1+4x) dx | (2- #) dæ -1 |x – 1| dx V4 – x² dx…

A: We have to find the definite integral

Q: Find the area bounded by the graphs of the indicated equations. Compute answers to three decimal…

A: In this question we have to find the bounded region.

Q: The arc length in the interval [0, x] is equal to (1/3)x + f(x). Find f(x) for x >= 0 given the arc…

A:

Q: (a) Suppose f"(x) = 0, what can you say about f (x)? Write it in general form. (b) Find the area of…

A: .

Q: 5. Consider the graph of y = 7-3x2. Calculate the area enclosed by the curve y= 7- 3x and the x-axis…

A: Area enclosed by the curve y=fx and x-axis between x=aand x=bis given by A=∫x=ax=bfxdx

Q: Find the area between the curve f(x) = x2 +11 and the x-axis from x = 3 to x = 7. The area is square…

A:

Q: Consider the region bounded above by g(x)=6x+6 and below by f(x)=7x−7. Find the area, in square…

A: Given,

Q: The tube cross-section shown has inner radius of 3 cm and outer radius 6 cm and within the tube…

A: This question is about application of derivative

Q: 7. Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter…

A:

Q: B. Integrating Factor Found by Inspection 1. x*y'=-x'y-csc(xy) 3

A:

Q: find the area bounded by y = sin(2x), y= cos(4x), x= 5, 12' the area is b y3 sq units. what is the…

A: To find the area bounded by the given curves

Q: How to determine f(x) and g(x) for area between curves? So if I'm trying to figure out the area…

A:

Q: The area shown below is bounded by the parabola y^2 = - x + C where C = 4.6. If using the vertical…

A: Vertical limit for integration is 0 to 4.6 y2 = -x+c  C = 4.6

Q: (a) Using x," as the right endpoint of each subinterval find the area between the graph of .2 and…

A: .

Q: Find the area bounded by the graphs of the indicated equations. Compute answers to three decimal…

A:

Q: Find the area bounded by the curve given by f(x) = -x² – x + 2 and the x-axis on the interval [–2,…

A: Given. Area bounded by the curve. f(x) = -x²-x+2 Y = 0 -2<x<1 To solve this we need to use…

Q: Esimate the area under a curve

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 2…

A: Given:  Air is being pumped into a spherical balloon so that its volume increases at a rate of 2…

Q: Estimate the area under the graph of f (x) 2 over the interval [2,5] using six approximating…

A:

Q: d the area bounded by the graphs of the indicated equations over the given interval. y=x2 - 24; y =…

A:

Q: 2. A hemisphere of radius 12 miches and base up is full of water that Funs out thrdugh an orifice of…

A: Given:  A hemisphere tank of radius (R) = 12 in =0.348 meter Area of orifice (a) = 1 in2 =0.00064516…

Q: 3 Estimate the minimum number of subintervals to approximate the value of | (4x +6) dx with an error…

A:

Q: 61. Does x" dx get larger or smaller as n increases? Explain graphically.

A:

Q: *7. Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter…

A:

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

A: Let's find.

Q: 5. Water is pouring into a conical vessel 15 cm deep and having a radius of 3.65 cm across the top.…

A:

Q: The area of the region in the first quadrant bounded below by the curve y=e* and above by the curve…

A: To find the area

Q: Si f(x) dx represents the signed area between the curve y = f (x) and the x-axis between x = a and x…

A:

Q: 7. 'Find the area of the region enclosed by the graphs of the equations y = cos x, y = sin x ,x = 0,…

A: Here required area is given by taking integration of (upper curve - lower curve) and limit from 0 to…

Q: NOTES A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 4…

A: In the given question above we have to find the height and the rate of water level rising.