Integration quiz 1
 Find the area of the region bounded by:a) y = sinx, the x-axis, x = 0 and x = πb) the axes and y = √ 9 - xunit2unit2 c) How long will it take for the particle's velocity to increase  o 45 m/s?b) Find the velocity of the particle after 3 seconds.a) State the initial velocity of the particle.The velocity of a particle travelling in a straight line is given by  v(t) = 50 - 10e-0.5t, where t ≥ 0, t in seconds.m/ssm/s( round off to 1 decimal place)( round off to 1 decimal place) ∫∫∫141( x -   e 1 - x  dx =π/600sin (3x) dx = √x  3  ) dx =Round all answer to 1 decimal place. The approximate value of ∫Given the graph of f(x)-11f(x) dx  = ∫(lnx)4(lnx)4( lnx )344xx+ C+ C=(A)(B)(lnx)4(lnx)444x++x21x21+ C+C(C)(D) ∫(A)6x2 - 2x2x3 - x2(C) ln | 2x3 -x| + C(B) ln | 6x2 -1| + C(D) 2 ln | x| + C4x3 - 2x2x3 - xdx =+ C The mean value of a function f(x) from a to b is given by (A)(B)(D)(C)f(a) + f(b)f (a) + 2f (∫∫b - a2ababf(x) dxf(x) dx4a+b2) + f(b) The marginal profit for producing x dinner plates per week is given by P'(x) =15 - 0.03x dollars per plate. If no plate are made then a loss of \$650 each week occur. Find the profit function P(x) , and hence findThe maximum profit:  \$ displacement of the particleA particle is initially at the origin and moving to the right at 5 cm/s. It accelerates with time according to a(t) = 4 - 2t cm/s. For the first 6 seconds of motion, determine thetotal distance travelled(round to the second decimalplace)cmcm Find the total area of the regions contained by f(x) = x3 + 2x2 - 3x and the x - axis(round to the second decimal place)unit2 Physically, integrating (A) area to the right of point a(B) displacement of a particle from a to b(C) area under the curve from a to b(D) total distance travel during the time b - a∫abf(x) dxmeans finding the Find the area  under f(x) from x =1 to x = 3(round to the second decimal place)y = lnx Find the area of the shaded region(round to the second decimal place) Rotate y = sin x (0 ≤ x ≤ π)around the x - axis to getthe solid below . Findthe volume of the shape(round the the second decimal place).unit2 18x6 - 12x4 + 2x290x4 - 36x2 + 2If F' = f and f(x) = 18x5 - 12x3 + 2x, which of the following could be F(x)?3x6 - 4x4 + x2 + 53x6 - 3x4 + x2 + 1  The area of the shaded region is(decimal) Find the area of the shaded region:(round to 2nd decimalplace)
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