Advertisements
Advertisements
Question
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Advertisements
Solution
\[\int\left( \frac{1 - \sin x}{\cos^2 x} \right) dx\]
\[ = \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos^2 x} \right)dx\]
\[ \int\left( \frac{1}{\cos^2 x} - \frac{\sin x}{\cos x} \times \frac{1}{\cos x} \right) dx\]
\[ = \int\left( \sec^2 x - \sec x \tan x \right) dx\]
\[ = \tan x - \sec x + C\]
APPEARS IN
RELATED QUESTIONS
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/("x" log "x")`dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int cos^3x dx` = ______.
`int (logx)^2/x dx` = ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
