Applications of Integrals
Math ⇒ Calculus
Applications of Integrals starts at 12 and continues till grade 12.
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See sample questions for grade 12
Find the area between y = cos(x) and y = sin(x) from x = 0 to x = π/2.
Find the area enclosed between y = x and y = x2 from x = 0 to x = 1.
Find the area inside the circle r = 2 in polar coordinates.
If a region is bounded by y = x2 and y = 4, what is the area between the curves from x = -2 to x = 2?
Find the area inside the circle r = 2 in polar coordinates.
If a tank is being filled at a rate r(t) = 5t liters per minute, how much water is added between t = 0 and t = 4 minutes?
If the acceleration of a car is a(t) = 4t, and its initial velocity is 2 m/s, what is its velocity at t = 3 seconds?
If the density of a rod of length L is given by ρ(x) = 2x, what is the total mass of the rod from x = 0 to x = 3?
Which of the following integrals gives the length of the curve y = f(x) from x = a to x = b? (1) ∫ab f(x) dx (2) ∫ab √[1 + (f'(x))2] dx (3) ∫ab [f(x)]2 dx (4) ∫ab f'(x) dx
Which of the following integrals represents the area under the curve y = f(x) from x = a to x = b? (1) ∫ab f(x) dx (2) ∫f(a)f(b) x dy (3) ∫ab x dx (4) ∫ab f'(x) dx
Which of the following is NOT a step in finding the area between two curves? (1) Find the points of intersection. (2) Integrate the difference of the functions. (3) Multiply the functions together. (4) Set up the definite integral.
Which of the following is NOT an application of definite integrals? (1) Finding the area under a curve (2) Calculating the volume of a solid of revolution (3) Determining the slope of a tangent (4) Computing the work done by a variable force
The area between the curves y = x2 and y = x + 2 from x = 0 to x = 2 is _______.
The area of the region bounded by y = |x| and y = 2 from x = -2 to x = 2 is _______.
The area under the curve y = 1/x from x = 1 to x = e is _______.
The area under the curve y = 2x + 1 from x = 1 to x = 3 is _______.
True or False: The area between two curves can be found by integrating with respect to y instead of x.
True or False: The area between two curves y = f(x) and y = g(x) from x = a to x = b is given by ∫ab |f(x) - g(x)| dx.
True or False: The area under a curve can be negative if the curve lies below the x-axis.
True or False: The definite integral can be used to find the average value of a function over an interval.
