# Applications of Integrals

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## Area under curve, area between two curves, volume of a solid revolution, average value of a function, distance and velocity and acceleration

Created Date 06.05.20
Last Updated 06.08.20
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Topics of this game:
• What is the formula for the area between two curves?
• What is the formula for solids of revolution around the x-axis?
• Which of the following does NOT use integrals?
• What is the formula for the average value of a function?
• What is the area under the curve y=3x²-3 from x=1 to x=2?
• What is the area under the curve y=eˣ-1 from x=0 to x=3
• What is the area under the curve y=sin(x)+1 from x=-π/2 to x=3π/2?
• What is the area under the curve y=1/x+4 from x=5 to x=10?
• What is area between the curves y=sqrt(x+3) and y=x²+1?
• What is the area between the curves y=2x⁴+3 and y=-x²+5?
• What is the area between the curves x=y²-5 and x=y+5?
• What is the volume of a solid created by revolving the region bounded by y=2x²+2 and y=6x about the x-axis?
• What is the volume of a solid created by revolving the region bounded by y=sqrt(x) and y=0.5x² about the x-axis?
• What is the volume of a solid created by revolving the region bounded by x=(y-2)² and x=-(y-2)²+4 about the y-axis?
• What is the average value of the function y=cos(x)+2 from x=-π to x=π?
• What is the average value of the function y=eˣ+3 from x=0 to x=2?
• What is the average value of the function y=4x⁵-1 from x=0 to x=1?
• What is the velocity of a particle at t=2 if the function for its acceleration is a(t)=3t²+4t+5 and the velocity at t=1 is 9?
• What is the displacement of a particle at t=4 if the function for its velocity is y=3x+7 and the displacement at t=2 is 19?
• What is the displacement of a particle at t=π/4 if the formula for its velocity is y=sec²(x)+2 if the displacement at t=0 is 3?
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