Advertisements
Advertisements
प्रश्न
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Advertisements
उत्तर
\[\int\left( \frac{1 - \sin x}{\cos^2 x} \right) dx\]
\[ = \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos^2 x} \right)dx\]
\[ \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos x} \times \frac{1}{\cos x} \right) dx\]
\[ = \int\left( \sec^2 x - \sec x \tan x \right) dx\]
\[ = \tan x - \sec x + C\]
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int sqrt(1 + sin2x) dx`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int secx/(secx - tanx)dx` equals ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int(1 + x + x^2/(2!))dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
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 sin^3x cos^3x dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
