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answer: (pi/4) - (1/2) more explanation on this area question
evaluate integral of (x ² +3x) with limits 1 to 3 using summation (limit of a sum)
answer: (62/3) explanation of integration by limit of sum question
evaluate integral of [ x*exp(x)] / (x+1) ² dx
answer: exp(x) / (x+1) + C explanation on integration by parts of exp(x)[f(x) + f '(x)] form
∫ { [log x] / x² } dx log x refers to lnx
answer: -(1+ln x ) /x +C explanation on integration by parts for ∫ { [log x] / x² } dx
∫ dx / [ (x-2) (1 + x²)]
answer:(1/5)ln(x-2) -(1/10)ln(1 + x²) -(2/5)arctan(x)+C explanation on integration by partial fraction
problem on matrices
answer: (x= -1) explanation of matrix problem
problem on determinant
explanation of determinant problem
solve x+y = 2 ; 2y-z = 0 ; -x-y+z = -1 using cramer's rule (using determinants)
answer : x = 3/2 , y =1/2 , z=1 explanation on solution of equations using cramer's rule
solve 3x+4y = 17 , -4x+3y =44 using matrix inversion
answer: x = -5; y =8 explanation on solving system of equations using matrix inversion
solve cos ² x (dy/dx) + y = tanx
answer : y = tanx - 1 + C exp(-tanx) explanation
if y = x sinx , find dy/dx from first principles
answer: dy/dx = xcosx +sinx explanation of first principle
show that the semivertical angle of a right circular cone
of maximum volume and given slant height is tan ֿ¹(√2 )
explanation of maxima / minima problem
show that the height of a closed cylinder of given volume and minimum surface area
is equal to its diameter explanation of minimising surface area
There is a figure (norman window) in which a rectangle is surmounted by a semicircle with diameter along one side of the rectangle .If the perimeter is given find the radius of the semicircle if the area is to be maximum (maximum amount of light is to be admitted into the room) explanation
A piece of string 28m long is to be cut into two pieces, one piece is to be made into a circle and the other
the boundary of a square. How should the string be cut if the sum of the areas of the two figures is to be a minimum answer and explanation
find the equation of the tangent at t = pi/3 on the curve x=2cost , y = 3sint
answer: 3x + 2ysqrt(3) =12 explanation of finding equation of tangent
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notes on hyperbolic function
revision problems in some topics for cbse isc mathematics
other problems on applications of integration like area ,volume etc
integration formulae
problems on integration
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list of formulae and notes on some math topics
formulae on sequences and series
(trig. formulae)
(integration formulae)
(other math problems without classification) or problem index
(formulae on differentiation)
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