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Definite Integrals & Area · Question 25 of 71

Question 25

MediumOriginal question

Evaluate ∫0π2cos⁡x1+sin⁡x dx\int_0^{\frac{\pi}{2}} \frac{\cos x}{1 + \sin x}\,dx.

Options for question 25

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The top is the derivative of the bottom, so an antiderivative is log⁡(1+sin⁡x)\log(1 + \sin x).

  2. log⁡2−log⁡1=log⁡2\log 2 - \log 1 = \log 2.

Worth noting

1 treats the integral as ∫0π/2cos⁡x dx\int_0^{\pi/2}\cos x\,dx, ignoring the denominator.

Concept
A derivative over its function, with limits
Typical time
90 s
Your time
—
The rule this testsSubstitution and by parts with limits
Practise this chapter →

Ten questions from Definite Integrals & Area, at your own pace.

Practise this chapter →

Ten questions from Definite Integrals & Area, at your own pace.