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For -1 < x < 1 the function sin⁻¹x has no obvious… | StemPy Lab
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For -1 < x < 1 the function sin⁻¹x has no obvious product in it. Treating it as sin⁻¹x · 1, which is its antiderivative, apart from the constant?
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High School (11–12)
Functions and Calculus › Integrals
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Created by
StemPy Lab
For
−
1
<
x
<
1
-1 < x < 1
−
1
<
x
<
1
the function
sin
−
1
x
\sin^{-1}x
sin
−
1
x
has no obvious product in it. Treating it as
sin
−
1
x
⋅
1
\sin^{-1}x \cdot 1
sin
−
1
x
⋅
1
, which is its antiderivative, apart from the constant?
x
sin
−
1
x
+
1
−
x
2
x\sin^{-1}x + \sqrt{1 - x^2}
x
sin
−
1
x
+
1
−
x
2
x
2
2
sin
−
1
x
\dfrac{x^2}{2}\sin^{-1}x
2
x
2
sin
−
1
x
1
1
−
x
2
\dfrac{1}{\sqrt{1 - x^2}}
1
−
x
2
1
x
sin
−
1
x
−
1
−
x
2
x\sin^{-1}x - \sqrt{1 - x^2}
x
sin
−
1
x
−
1
−
x
2
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← A student notices that sin x is the derivative of -cos x, and she wonders about ∫ eˣ(sin x + cos x)dx. Which result is correct?
The fraction (2x² + 3)/(x² - 1) has top and bottom of the same degree. After dividing, the integral is found by partial fractions. What is the antiderivative on x > 1, apart from the constant? →
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Functions and Calculus › Integrals
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