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sql server reporting services barcode font SOLUTION in Software
SOLUTION QR Code 2d Barcode Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Denso QR Bar Code Generation In None Using Barcode creation for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications. Because of the complicated nature of f(x), it is faster to use NIntegrate.
Decode QR Code In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. QRCode Creator In Visual C# Using Barcode generator for Visual Studio .NET Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. f[x_]= Exp[Sin[x]]; F1[x_] NIntegrate[f[t], {t, 0, x}] F2[x_] NIntegrate[f[t], {t, 1, x}] F3[x_] NIntegrate[f[t], {t, 2, x}] Plot[{F1[x], F2[x], F3[x]}, {x, 0, 2 o}] Painting Denso QR Bar Code In .NET Framework Using Barcode printer for ASP.NET Control to generate, create QR Code ISO/IEC18004 image in ASP.NET applications. Print QRCode In VS .NET Using Barcode maker for .NET Control to generate, create QR Code image in VS .NET applications. 8 6 4 2 Create QR In VB.NET Using Barcode creation for .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications. EAN / UCC  14 Printer In None Using Barcode generator for Software Control to generate, create GTIN  128 image in Software applications. 1 2 4 Print Barcode In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. USS Code 39 Maker In None Using Barcode maker for Software Control to generate, create USS Code 39 image in Software applications. 9.16 Consider the semicircle x2 + y2 = 16, y 0 shown in the figure. Find the height, h, so that the shaded y area is half the area of the semicircle. UPCA Supplement 5 Printer In None Using Barcode maker for Software Control to generate, create UCC  12 image in Software applications. Paint Barcode In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. SOLUTION
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Encode Linear Barcode In Java Using Barcode generation for Java Control to generate, create Linear Barcode image in Java applications. Barcode Generation In None Using Barcode generator for Office Excel Control to generate, create bar code image in Excel applications. By subdividing the yaxis and taking advantage of symmetry, we obtain the following representation for A(h), the shaded area: A(h) = 2 x ( y)dy where x ( y) = 16 y 2 x[y_]= 16 y 2 ; A[h_]= 2 x[y] y; Compute the total area inside the semicircle. (Since we know a formula for the area of a circle, this is a good check for errors.) A[4] 8 To approximate the solution, draw a graph of A(h): Plot[A[h], {h, 0, 4}] Integral Calculus
It appears that half the semicircular area, 4 12.5, corresponds to a value of h near 1.5. We finish the job with FindRoot. FindRoot[A[h] 4 , {h, 1.5}] {h 1.61589} 9.17 The curve shown is the parabola y = 9 x2. Find h so that the shaded area is twothirds the total area bounded by the curve and the xaxis. y SOLUTION
Solve[y 9 x , x] {{x
9 y , x 9 y
6 4 2 h x[y_]= 9 y; A[h_]= 2 x[y] y; 0 totalarea = A[9] 3 36 Plot[A[h], {h, 0, 9}, AxesLabel { ,"A(h) }] "h" " A (h) 35 30 25 20 15 10 5 2 4 6 8 h
2 1 Twothirds of the total area of 36 is 24 and appears to correspond to a value of h near 5.
FindRoot[A[h] (2/3) totalarea, {h, 5}] {h 4.67325} Integral Calculus
9.18 Find a point on the parabola y = x2 which is five units away from the origin along the curve.
SOLUTION
The length of arc of a function, f(x), from x = a to x = b is L = 1 + [ f '( x )]2 dx . Obviously there are two points. We shall a find the point that lies in the first quadrant. f[x_] = x2; s[x_] = 2 1 + f'[t] t; Plot[s[x], {x, 0, 3}, AxesLabel {"x", "s(x)"}] s (x) 8 6 4 2 x The graph shows s(2) 5. solution = FindRoot[s[x] 5, {x, 2}] {x 2.08401} x = x /. solution; {x, f[x]} {2.08401, 4.34308} 9.19 A mixing bowl is a hemisphere of radius 5 in. Determine the height of 100 cubic inches of liquid. SOLUTION
The equation of the hemisphere in three dimensions is x 2 + y 2 + z 2 = 25, z 0. Its intersection with the plane z = z0 is the circle x 2 + y 2 = 25 z02, whose radius r = 25 z02 and whose area r 2 = (25 z02 ) . Integrating with respect to z, the volume of the shaded region is V (h) = been replaced by z for convenience.) v[h_] = o 5+ h 5
(25 z 2 ) dz. (z0 has
h x 5
3 5 h2 h 3
5+h
(25 z2) z
As a check, v[5] should give the volume of the hemisphere. T he volume of the hemisphere is 2 r3 = 2 (53 ) = 250 . 3 3 3 v[5] 250 3 Plot v as a function of h. Plot[v[h], {h, 0, 5}, AxesLabel {"h", "v[h]"}] Integral Calculus
v [h] 250 200 150 100 50 h
Since v[h] is a polynomial function, we can use NSolve to determine the approximate solution to the problem. (From the graph, it looks like h is near 3.) NSolve[v[h] 100] {{h 2.34629}, {h 2.79744}, {h 14.5489}} Obviously, the only realistic solution is h = 2.79744 in. 9.20 An underground fuel tank is in the shape of an elliptical cylinder. The tank has length l = 20 ft, semimajor axis a = 10 ft and semiminor axis b = 5 ft. b To measure the amount of fuel in the tank, we insert a stick vertically through the center of the cylinder until it touches the bottom of the tank and measure how high the a a fuel level is on the stick. How far from the end of the stick should a mark be placed to indicate that only 500 cubic h feet of fuel remain

