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Finding areas by integration PDF

Find the area of the region bounded by the graph, Find the volume of the solid generated by rotating the region bounded by about the line, Determine if the improper integral converges and, if so, determine its value, Evaluate the indefinite integral, Evaluate A force of 10 lbs is required to hold a spring stretches 4 inches beyond its natural length. How much work is done to stretches it from its natural length to 5 inches beyond its natural length?, Integrate, Find the interval of convergence for the power series, Does the series converges and, if so to what?, Use a series to evaluate the limit

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Added on  2021-04-22

Finding areas by integration PDF

Find the area of the region bounded by the graph, Find the volume of the solid generated by rotating the region bounded by about the line, Determine if the improper integral converges and, if so, determine its value, Evaluate the indefinite integral, Evaluate A force of 10 lbs is required to hold a spring stretches 4 inches beyond its natural length. How much work is done to stretches it from its natural length to 5 inches beyond its natural length?, Integrate, Find the interval of convergence for the power series, Does the series converges and, if so to what?, Use a series to evaluate the limit

   Added on 2021-04-22

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QUIZ # 7 Problems(10 questions, 10 points each)1.Find the area of the region bounded by the graph off(x)=2x2+8g(x)=4x+14,attheintervale[3,6]Solution – Area of region bounded by the graph is given by,ab|f(x)g(x)|dxf(x)=2x2+8g(x)=4x+14Therefore, Area, A = 36|2x2+84x+14|dxSolving the integral, we get A = 290/3 = 96.672.Find the volume of the solid generated by rotating the region bounded by y=4xx2about the line x=5.Solution – Given equation, y=4xx2About the line x = 5 means x = 0 to 5Volume = = 130.93.Determine if the improper integral converges and, if so, determine its value: 08138xdxSolution – The problem point is the upper limitSolving for,
Finding areas by integration PDF_1
0t138xdx = 3(8t)232+6Now Solving for, limt83(8t)232+6 = 1.61 The limit exists and is finite and so the integral converges and the integral's value is1.614.Evaluate the indefinite integral xln(x)dxSolution –Applying Integration by parts,u = ln x and v = xSolving, x2dx = x24Therefore, xln(x)dx5.Evaluate 134x2+5xdxSolution: Applying Integration by partsu = 4x2+5 and v = 1xSimplifying,
Finding areas by integration PDF_2
Substituting in the above equation,Computing for boundariesPlugging in x = 1= 585And, Substituting all the values, = 30.666.A force of 10 lbs is required to hold a spring stretches 4 inches beyond its natural length. How much work is done to stretches it from its natural length to 5 inches beyond its natural length?Solution – Force = kx10 = k (1/3) [4 inches = 1/3 feet]K = 30So, f (x) = 30xWork done W = 00.41666730xdx = 30[x22¿= 30 0.41666722 = 2.6 ft.lb7.Integrate e3xe6x+36dx
Finding areas by integration PDF_3

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