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Find I = ∫ sec³ x dx. The answer is I = ½ [ log(sec x + tan x) + sec x tan x ]. * Here is how we may find it: Letting s = sec x, and t = tan x, we have, s² = 1 + t², dt = s² dx = (1 + t²) dx, and ds = st dx. Then, we obtain, dI = s³ dx = s dt. * Now, d(st) = s dt + t ds = dI + t ds = dI + st² dx = dI + s(s² - 1)dx = dI + s³ dx - s dx = 2dI - s dx; whence, 2dI = s dx + d(st). * Also, we have, s = (s² + st) / (s + t), whence s dx = (s² + st) dx / (s + t) = (dt + ds) / (s + t) = d(s + t) / (s + t) = d log(s + t). This gives us, 2dI = d log(s + t) + d(st). Integrating, we easily obtain, I = ½ [ log(s + t) + st ], which is the answer we sought. * Checking that we have arrived at the correct answer, we differentiate back: d(st) / dx = (st)'= st' + ts' = s³ + st² = 2s³ - s. d log(s + t) / dx = log'(s + t) = (s + t)' / (s + t) = (st + s²) / (s + t) = s. Thus, 2I' = [ st + log(s + t) ]' = 2s³; and I' = ½ [ st + log(s + t) ]' = s³, confirming that our answer is correct.
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Does a secant tangent angle pass through the center of the circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
A secant line is a line that intersects a circle at exactly one point?
false
Can a line be tangent to one circle and a secant to the other in concentric circles?
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.
How many ml in a cm cubed?
One
What is integral in math?
There are two main definitions. One defines the integral of a function as an "antiderivative", that is, the opposite of the derivative of a function. The other definition refers to an integral of a function as being the area under the curve for that function.
A secant tangent passes through the center of a circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Is every diameter of a circle is a secant of the circle?
If one is, they all are!
A secant is a line or segment that passes through a circle in one and only one place?
It would be False because a secant is a line or segment that passes through a circle in two places.
Does a secant tangent angle pass through the center of the circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Where can you find an integral table?
One can find many examples of integral tables online. Sites such as Mathwords, Math2org, Cobalt and SOSMath have many examples available for use as well as instructions on how to use them.
Areas where projection touchs more than one point?
secant
How many centimeter cubed are there in one centimeter cubed?
One exactly
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
A secant line is a line that intersects a circle at exactly one point?
false
How many centimeters cubed are in one meter cubed?
1,000,000
What is one cubed?
one
How do you convert pound per foot cubed to pound per square inch?
If you are trying to find pound per square inch cubed, you would just divide the pound per foot cubed by 12x12x12 (1,728). One foot cubed is equal to a block of cubed inches 12x12x12, correct? Then you just add on the "pound per" measurement and you have your answer.
