Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int sin 4x cos 3x dx`
उत्तर
`int sin 4x cos 3x dx`
= `(1)/(2)int sin 4x cos 3x dx` ...[∴ 2sinA.cosB = sin (A + B) + sin(A - B)]
= `(1)/(2)int [sin (4x + 3x) + sin (4x - 3x)]dx`
= `(1)/(2) int sin 7x dx + (1)/(2)int sin x dx`
= `(-1)/(2)((cos 7x)/7) + ((-1)/(2))cos x + c`
= `-(1)/(14)cos 7x - (1)/(2) cos x + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate :`intxlogxdx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int cot^2x "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Write `int cotx dx`.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
