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Calculus, SPEC2 2014 VCAA 12 MC

If  `(dy)/(dx) = sqrt((2x^6 + 1))`  and  `y = 5`  when  `x = 1`, then the value of `y` when  `x = 4`  is given by

  1. `int_1^4(sqrt((2x^6 + 1)) + 5)\ dx`
  2. `int_1^4sqrt((2x^6 + 1))\ dx`
  3. `int_1^4 sqrt((2x^6 + 1))\ dx + 5`
  4. `int_1^4sqrt((2x^6 + 1))\ dx - 5`
  5. `int_1^4(sqrt((2x^6 + 1)) - 5)\ dx`
Show Answers Only

`C`

Show Worked Solution
`F(b)-F(a) ` `= int_a^b sqrt((2x^6 + 1))\ dx`
`F(b)` `= int_a^b sqrt((2x^6 + 1))\ dx + F(a)`
`:. F(4)` `= int_1^4 sqrt((2x^6 + 1))\ dx + F(1)`
  `= int_1^4 sqrt((2x^6 + 1))\ dx + 5`

 
`=> C`