Here is a Multi choice problem on Integration, Integrating a trigonometric functions and finding its derivative. You can find similar set of questions at Tutor Vista Blogs.
Topic : Integrating Trigonometric value.
Calculation in the solution will help you to identify correct choice and get reasons for, why remaining choices are incorrect.
Problem : If y = 0∫x2Cos t dt, then dy/dx = ?
a. 2x Cos(x2)
b. Cos(x2)
c. 2x Sin (x2)
d. Sin (x2)
Solution :
choice a is correct.
y = 0∫x2Cos t dt
Let u = x2
= Cos (u) * 2x
= 2x Cos (x2)
Choice b is incorrect because of applying the fundamental theorem of calculus without using the chain rule.
Choice c is incorrect because of wrong application of fundamental theorem of calculus.
Choice d is incorrect because of wrong application of fundamental theorem of calculus.
Topic : Integrating Trigonometric value.
Calculation in the solution will help you to identify correct choice and get reasons for, why remaining choices are incorrect.
Problem : If y = 0∫x2Cos t dt, then dy/dx = ?
a. 2x Cos(x2)
b. Cos(x2)
c. 2x Sin (x2)
d. Sin (x2)
Solution :
choice a is correct.
y = 0∫x2Cos t dt
Let u = x2
= Cos (u) * 2x
= 2x Cos (x2)
Choice b is incorrect because of applying the fundamental theorem of calculus without using the chain rule.
Choice c is incorrect because of wrong application of fundamental theorem of calculus.
Choice d is incorrect because of wrong application of fundamental theorem of calculus.
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