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For ∫ sin(√x) dx
let y = √x = x1/2
→ dy = 1/2 x-1/2 dx
→ 2x1/2 dy = dx
→ 2y dy = dx
→ ∫ sin(x1/2) dx = ∫(sin y) 2y dy
Now:
∫ uv dx = u∫v dx - ∫(u'∫v dx) dx
→ ∫(sin y) 2y dy = ∫2y sin y dy
= 2y ∫sin y dy - ∫(2 ∫sin y dy) dy
= -2y cos y + 2 sin y + C
= 2 sin y - 2y cos y + C
→ ∫ sin(√x) dx = 2 sin(√x) - 2(√x) cos(√x) + C
What else can I help you with?
What is the integration of root sinx?
The integral of root(sin(x)) is -2 time the elliptic integral of the second order of .25(pi-2x) at 2. For this and other integrals, go to http://integrals.wolfram.com/index.jsp?expr=sqrt(sin(x))&random=false For more information on the elliptic integral functions, go to http://en.wikipedia.org/wiki/Elliptic_integral Hope this helps!
How do you integrate ln x over square root of x?
x/sqrt(x)=sqrt(x) integral sqrt(x)=2/3x3/2
What is the square root of the fifth root of x?
The square root of the fifth root of x is the tenth root of x.
Integral of sinx cosx sin2x cos3x dx?
Integral[sin(x)cos(x)sin2(x)cos3(x)] dxgather termsintegral[sin3(x) cos4(x)] dxpull one sin(x) as sin is oddintegral[sin2(x) cos4(x) sin(x)] dxusing trig identitiesintegral[(1 - cos2(X)) cos4(x) sin(X)] dxu substitutionu = cos(x)du = - sin(x) dxsointegral[(1 - u2)) (u4) - du] dx- integral[(1- u2)) u4 du] dx= u - 1/3u3 + 1/5u5 du= cos(x) - 1/3cos3(x) + 1/5cos5(x) + C============================
Formula for square root?
Square root of x = x^0.5
What is integral square root of sin x.dx?
-cos(x) + constant
Integral of sin square x times cos square x?
(1/8)(x-sin 4x)
What is the integral of the square root of x minus 1 squared?
the integral of the square-root of (x-1)2 = x2/2 - x + C
What is the integration of cotx?
The integral of cot (x) dx is ln (absolute value (sin (x))) + C. Without using the absolute value, you can use the square root of the square, i.e. ln (square root (sin2x)) + C
What is the integral of x to the half?
square root x
What is the integral of e raised to the square root of x divided by the square root of x?
replace square root o x with t.
How do you differentiate cosine square root of x?
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
Integral of 1 divided by sinx cosx?
Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C
Why sin integral is cos?
sin integral is -cos This is so because the derivative of cos x = -sin x
What is the limit as approaches infinity of the square root of x multiplied by sin of x?
The sequence sqrt(x)*sin(x) does not converge.
What is the derivative of square root 2 sin x?
It is not totally clear to what the square root applies*; if just the 2, then: d/dx ((√2)sin x) = (√2) cos x if all of 2 sin x, then: d/dx (√(2 sin x)) = cos x / √(2 sin x) * for the second version I would expect "square root all of 2 sin x" but some people would write as given in the question meaning this, so I've given both just in case.
What is the integral of secant squared square root x?
tan(sqrtX) + C
