Advertisements
Advertisements
प्रश्न
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Advertisements
उत्तर
Let I = `int (3- 2sinx)/(cos^2x)*dx`
= `int(3/(cos^2x) - (2sinx)/(cos^2x))*dx`
= `3 int sec^2x*dx - 2int sec x tanx*dx`
= 3 tan x – 2 sec x + c.
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x sin 3x.
Integrate the function in `x^2e^x`.
Integrate the function in x log x.
Integrate the function in (sin-1x)2.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in x (log x)2.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^2.log x.dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : sec4x cosec2x
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
`int 1/sqrt(2x^2 - 5) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int(x + 1/x)^3 dx` = ______.
Evaluate `int 1/(4x^2 - 1) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate the following:
`int_0^pi x log sin x "d"x`
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int(1-x)^-2 dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
Solve the following
`int_0^1 e^(x^2) x^3 dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
