Simple Substitution

Calculus Level 3

Evaluate: ∫ 1 3 − 2 x 2 d x \displaystyle \int \dfrac{1}{\sqrt{3-2x^2}} dx

None of the above 1 2 arcsin ⁡ ( 2 3 x ) \frac{1}{{2}}\arcsin(\frac{\sqrt{2}}{\sqrt{3}}x) 1 3 arcsin ⁡ ( 3 2 x ) \frac{1}{{3}}\arcsin(\frac{\sqrt{3}}{\sqrt{2}}x) 1 2 sin ⁡ ( 2 3 x ) \frac{1}{\sqrt{2}}\sin(\frac{\sqrt{2}}{\sqrt{3}}x)

Asher Joy by Asher Joy , 22, USA

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1 solution

Anoir Trabelsi
Apr 18, 2014

substitute x by sqrt(3/2) sin theta :)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

The correct answer would be,

I = 1 2 ⋅ arcsin ⁡ ( 2 x 3 ) + C I=\dfrac{1}{\sqrt{2}}\cdot \arcsin \left( \dfrac{\sqrt{2}x}{\sqrt{3}} \right)+C

where C C is the integrating constant.

NOTE: arcsin ⁡ x \arcsin x is also written as sin ⁡ − 1 x \sin^{-1} x . Both have the same meaning.

Prasun Biswas - 6 years, 4 months ago

Yes :). None of the choices were correct.

Asher Joy - 7 years, 1 month ago

I mistook sin as arc(sin)!

Mayank Holmes - 7 years, 1 month ago

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