Application of Integration

Application of Integration posted on: 18 Jan, 2012 | updated on: 05 Jun, 2012

Topics Covered in Application of Integration

Velocity and Distance Problems Involving Motion Along a Line Area of Region | Area of a Region Area Between Curves | Areas Between Curves Volumes of Solid of Revolutions Area of Region Bounded by Parametrically Defined or Polar Curves Arc Length | Calculus Arc Length Velocity and Acceleration Vectors of Planar curves Other Applications involving the use of Integral of Rates

Velocity and Distance Problems Involving Motion Along a Line posted on: 13 Mar, 2012 | updated on: 05 Jun, 2012

Area of region posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Calculate the area of the region given by the following lines: a + b = 2, a â&#x20AC;&#x201C; b = - 1, a + 2 y = 2 ?

Find the area of the Region bounded by the following set of equations: m = n 3 – 6 n 2 – 1 6 n and m = 8 n + 2 n 2 – n 3?

Find the area of the region enclosed between the following curves, a = b 2 â&#x20AC;&#x201C; 2 b + 2 and a = - b 2 + 6 ?

Find the area enclosed by the ellipse: X / m 2+ y / n 2 = 1?

Find the area of the region bounded by the curves y=x and x2 +y 2 = 32, common with first quadrant?

Find the area between the given curves, x 2 + y 2 = 4 and ( x â&#x20AC;&#x201C; 2 ) 2 + y 2 = 4?

Find the area of the curve x = 2 - 2 sin ??

Find the area between the curves n = 1 and n = 2 sin ??

Find the area bounded by the following equations: L (x) = 4 x â&#x20AC;&#x201C; x2 and n (x) = 5 - 2x?

Calculate the area underneath the curve y = x2 + 2 from x = 1 to x = 2?

FAQ of Area of Region | Area of a Region

Find the Area of the Region? Arc Length of a Circle

Area between curves posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Volumes of Solid of Revolutions posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Calculate the volume if area bounded by curve is y = x3 + 1, limits are x = 0 and x = 3 and ‘x’ axis are rotated around x – axis?

Area of Region Bounded by Parametrically Defined or Polar Curves posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Arc Length posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Determine the arc length of y = log (cosec x) where x lies between 0 to ?/4?

Calculate the arc length of the function f(x) = (x 5) / 2 over the interval [0,1]?

Calculate the arc length of the circle whose radius is given as 5m and central angle is 300?

Calculate the arc length of y = log (sec t) between 0 ? t ? ?/2?

Determine the length of the function x = (2 / 5) * (y â&#x20AC;&#x201C; 1) * (5 / 2) where y lies between 1 ? y ? 4?

Calculate the length of the function x = (1 / 2) y 3 for the values 0 ? x ? (1 / 2)?

Calculate the length of arc on the given curve y = (x)3, from point (-1 , -1) to (2 , 8)?

FAQ of Arc Length | Calculus Arc Length

Arc Length in Polar Coordinates Calculate Arc Length? Calculus Arc Length Formula

Velocity and Acceleration Vectors of Planar curves posted on: 06 Feb, 2012 | updated on: 24 May, 2012

If a particle is moving along a plane curve 'C' then calculate the velocity vector and acceleration vector. The plane curve 'C' is described by r(t) = 2 sin t/2 i + 2 cos t/2 j?

If a plane curve 'C' is represented by r (t) = (t2 â&#x20AC;&#x201C; 4)i + tj then find the velocity and acceleration vectors when t = 0 and t = 2?

Find the velocity and acceleration vectors if an object is moving along a curve 'C' represented by r (t) = ti + t3j + 3tk, t ? 0?

An object moves in xy plane at any time 't', the position of object is given by x(t) = t3 + 4t2, y(t) = t4 â&#x20AC;&#x201C; t3. Calculate the velocity vector when t = 1 and acceleration vector when t = 2?

A body is moving in a plane and its position at any time t ? 0 is (sin t, t2/2). Calculate the velocity vector and acceleration vector of the moving body?

If an object moves in a plane and has position vector r (t) = [sin (3t), cos (5t)]. Calculate the velocity and acceleration vectors?

If a particle moves along a plane curve having position vector r (t) = [4 sin t, 9 cos t]. Calculate the velocity vector and acceleration vector?

An object moves in x-y plane at any time 't', the position of object is given by x(t) = t4 + 3t, y(t) = t3 â&#x20AC;&#x201C; t2. Calculate the velocity vector when t = 2 and acceleration vector when t = 3?

A particle moves in x-y plane at any time 't', the position vector of particle is given by x(t) = t3 +1, y(t)= t2. Calculate the velocity vector and acceleration vector?

When a body is moving in x-y plane at any time â&#x20AC;&#x2DC;tâ&#x20AC;&#x2122;, the position vector of body is given by x(t) = t5, y(t) = t3. Calculate the velocity vector and acceleration vector?

Other Applications involving the use of Integral of Rates posted on: 06 Feb, 2012 | updated on: 24 May, 2012

Calculate the amount of work done on a spring, when spring is compressed from its natural length of 1 unit to a length of 0.75 units, if the spring constant is equals to k = 16?

A spring is compressed by a force of 1200 N from its natural length of 18 units to a length of 16 units. Calculate the amount of work done in compressing it from 16 units to 14 units?

The temperature recorded during the day follows the curve T = 0.001 t4 â&#x20AC;&#x201C; 0.280 t2 + 25, where ' t ' is the number of hours from noon. (- 1 ? t ? 2). Calculate the average temperature of during the day?

A plate with right triangular base of 2.0 units and height 1.0 units is vertically submerged, with the top vertex 3.0 units below the surface. Calculate the force on one side of place?

The movement of proton in an electric field with acceleration a = 20 (1 + 2t)- 2, where time 't' is in seconds. Calculate the velocity as a function of time if v = 30 units / s when t = 0?

A flare is launched vertically upwards from surface at 15 unit / s. Calculate the height of flare after 2.5 s?

The electric current as a function of time is given by i = 0.3 â&#x20AC;&#x201C; 0.2 t, in a computer circuit. Calculate the amount of charge passes through a point in circuit in 0.50 s?

A 8.50 nf capacitor has a voltage of zero in an FM receiver. Calculate the voltage after 2.00 ?s if a current i = 0.042t (in mA) charges the capacitor?

The initial velocity of moving car is 5 mph and its acceleration is a ( t ) = 2.4 t mph for 8 seconds. Calculate the velocity of car when 8 seconds are up?

The initial velocity of a moving car is 5 mph with rate of acceleration a (t) = 2.4 t mph for 8 seconds. Calculate the distance covered by car during those 8 seconds?

The amount of force required to stretch a spring by 2 units beyond its natural length. Calculate the amount of work done to stretch the spring 4 units from its natural length?

Between the year 1970 to 1980, the rate of consumption of potato in a country was R (t) = 2.2 + 1.1 t millions bushels per year, while 't' are the years from beginning of 1970. Calculate the consumption of from start of 1972 to the end of 1973?

If the acceleration of a body is given by a = t2 + 1, between time interval t = 2 to t = 3, then calculate the velocity of the body in the given interval?

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