solving integral

Question

∫ ( t/(√(2t²-1) )dt=________

 

A) (-1/2)(√(2t²-1))+C

B) 4(√(2t²-1))+C

C) 8(√(2t²-1)+C

D) -( (1)/(4(2t²-1)) )+C

E) (1/2)(√(2t²-1))+C

 

Answer 1

Let u = 2t² -1  Then du = 4tdt   So, tdt = ¼du

 

Substitute into the integral:  ¼∫u^-½du = ¼(2u^½) + C

 

                                                                    = ½√(2t²-1) + C

 

ANSWER: (E)

Answer 2

We know that integrals are the opposite of derivatives.  So if we take the derivative of each answer choice, starting with choice C, one of these answer choices will give us a result of

 

t / √(2t² - 1)

 

 

We can also write this as

 

√(t² / (2t² - 1))