Applications of Integrals

Math ⇒ Calculus

Applications of Integrals starts at 12 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Applications of Integrals. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

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?

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 cross-sectional area of a solid perpendicular to the x-axis at x is A(x), what is the volume of the solid from x = a to x = b?

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?

If the rate of change of a quantity Q(t) is given by dQ/dt = 6t, and Q(0) = 5, what is Q(2)?

If the region bounded by y = x and y = x³ is rotated about the x-axis from x = 0 to x = 1, what is the volume of the solid formed?

If the region bounded by y = x² and y = 2x is rotated about the x-axis from x = 0 to x = 2, what is the volume of the solid formed?

If the region bounded by y = x² and y = 2x is rotated about the y-axis, what is the volume of the solid formed from y = 0 to y = 4?

If the region bounded by y = x² and y = 4 is rotated about the x-axis, what is the volume of the solid formed from x = -2 to x = 2?

If the region bounded by y = x² and y = 4 is rotated about the y-axis, what is the volume of the solid formed from y = 0 to y = 4?

If the velocity of a particle is given by v(t) = 3t², what is the displacement from t = 0 to t = 2?

A particle moves along a straight line so that its velocity at time t is v(t) = t² - 4t + 3 (in m/s). Find the total distance traveled by the particle from t = 0 to t = 4 seconds.

A region is bounded above by y = ln(x), below by y = 0, and on the sides by x = 1 and x = e. Find the area of this region.