Integral Calculus Answers

The table below gives the depth of water across a river measured at one metre
intervals between banks.
Distance (m) 0 1 2 3 4
Water depth (m) 0 0.5 1.6 0.9 0
Use the Trapezium rule to estimate the cross-sectional area of the river.
A river hydrologist estimates that at the place where this cross sectional data was
measured the average speed of water flow is 0.6m/s. Estimate the volume of water
which passes this section of the river in one minute.

find the area bounded by y=Inx,y=0 and x=e

find the area bounded by y=x^3+3x^2 and y=2x^2+4x

evaluate the intergration of (2-5X-x2)dx over (x^2-x-6)(x+2)

Find the area bounded by x= (y^2) - y and x=y-(y^2), take the elements of the area parallel to y-axis.

If x is an integer where 14 < x < 43, how many possible values are there for x?

find the area
a. y^2=-x; x=-2; x=-4
b. x^2 +y+4=0; y=-8 Take the elements of area parallel to the y-axis.
c. x^2 -y+1=0; x-y+1=0 Take the elements parallel to the x-axis.
d. x=4-y^2; x=4-4y

Evaluate the line integral [(2x-y+4)dx + (5y+3x-6)dy] around a circle of radius 4 with center at (0,0).

Evaluate the integral between (1,1) and (4,2): [(x+y)dx + (y-x)dy] Along
a) a straight line.
b) straight lines from (1,1) to (1,2) and then to (4,2).
c) the curve x = 2t^2 + t + 1, y = t^2 +1.

find the integral of ∫(((y-5)/(y^2+5y+6)