1003124406 Level: ACalculate the area of a plane region bounded by the graphs of the functions f(x)=x2+2x+2 and g(x)=6−x2.92115593
1103124405 Level: CLet a solid be obtained by rotating the blue triangle about the y-axis (see the picture). Find the volume of this solid.32π3296π100
1103124404 Level: CLet a solid be obtained by rotating the blue triangle about the x-axis (see the picture). Find such a value of a, that the volume of this solid is 48π.a=4a=2a=3a=6
1103124403 Level: BLet a solid be obtained by rotating the yellow region about the x-axis (see the picture). Find its volume.85.5π85.52727π
1103124402 Level: CFind such a real number a, that the area of the region highlighted in green equals 6 (see the picture).a=2a=1a=3a=4
1003068203 Level: BWhat is the volume of the solid that we get by rotating the curve y=1x2 about the x-axis on the interval [1;3]?2681π35−136π2881π35+136π
1003068202 Level: BThe value of the integral π⋅∫06[9−(x−3)2]dx is a number which represents:the volume of a sphere with the radius of 3cm.the volume of a sphere with the radius of 6cm.the volume of a sphere with the diameter of 3cm.the volume of a semi-sphere with the radius of 3cm.
1003068201 Level: BThe value of the integral 4π9∫03x2dx is a number which represents:the volume of a cone with the base radius of 2cm and the height of 3cm.the volume of a cone with the base radius of 3cm and the height of 2cm.the volume of a sphere segment which is a part of a sphere with the radius of 23cm and the height of 3cm.volume of a sphere segment which is a part of a sphere with the radius of 3cm and the height of 23cm.
1103068005 Level: AFind the missing real constant a so that the green area and the red area indicated in the picture do equal.a=−2πa=−32πa=−π2a=−3π