8073

Mathematics Integration Level: Misc Level

What are standard integrals and integrals of trignometric functions?


8072

Mathematics Integration Level: Misc Level

What are standard integrals and integrals of trignometric functions?


8071

Mathematics Integration Level: Misc Level

What are the fundamental notations of integral calculus, properties of definite integrals and solutions of differential equations?


8067

Mathematics Integration Level: Misc Level

What are the fundamental notations of integral calculus, properties of definite integrals and solutions of differential equations?


8042

Mathematics Integration Level: Misc Level

For f (x)=x^2 (5-7x^3)^4 find integral of f(x)


5828

Mathematics Integration Level: Misc Level

An open box with a square base is to be made out of a given quantity of cardboard whose area is c2 square units. Show that the maximum volume of the box is \frac{c^{3}}{6\sqrt{3}} cubic units.


5827

Mathematics Integration Level: Misc Level

Show that the semi-vertical angle of the right circular cone of given total surface area and maximum volume is Sins^{-1}\frac{1}{3}


5826

Mathematics Integration Level: Misc Level

Find the maximum volume of the cylinder which can be insrcribed in a sphere of radius 3\sqrt{3} cm. (Leave the answer in terms of \pi)


5825

Mathematics Integration Level: Misc Level

A closed right circular cylinder has a volume of 2156 cubic cm. What will be the radius of its base so that its total surface area is minimum? Find the height of the cylinder when its total surface is minimum. Take \pi=22/7


5824

Mathematics Integration Level: Misc Level

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top by cutting off squares from the corners and folding up the flaps. What should be the side of the square in order that the volume of the box is maximum?


5783

Mathematics Integration Level: Misc Level

An open box with a square base is to be made of given iron sheet of area 27 square meters. Show that the maximum volume of the box is 13.5 cubic meter.


5782

Mathematics Integration Level: Misc Level

Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube


5781

Mathematics Integration Level: Misc Level

Find the point on the parabola y2 = 4x which is nearest to the point (2,-8)


5780

Mathematics Integration Level: Misc Level

A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is p cm, show that the window will admit maximum possible light only when the radius of semicircle is \frac{p}{\pi+4} cm


5779

Mathematics Integration Level: Misc Level

A wire 10 meters long is cut into two parts. One part is bent into the shape of a circle and the other into the shape of an equilateral triangle. How should the wire be cut so that the combined area of the two figures is as small as possible?


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