Advertisements
Advertisements
प्रश्न
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
उत्तर
`int_0^3 f(x) dx = int_0^(pi/2) cos 2x dx + int_(pi/2)^3 dx`
`= (sin 2x/2)_0^(pi/2) + [3x]_(pi/2)^3`
`= [(sin 2 xx pi/2)/2 - (sin 2 xx 0)/2] + [(3 xx 3 - 3 xx pi/2)]`
`= 0 + 9 - (3pi)/2`
`= 9- (3pi)/2`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
`int logx/x "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int dx/(1 + e^-x)` = ______
`int (logx)^2/x dx` = ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int 1/(x(x-1)) dx`
