Lesson 8.5
8.5 Integrating functions of hyperbolic form Quiz: Pearson Edexcel Further Maths, Unit 8
20 questions
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Lesson 8.5, Integrating functions of hyperbolic form: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 8: Hyperbolic functions, written with Revision Ninja.
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The 20 questions
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What is the integral of 1/sqrt(x^2 + 1) with respect to x?
- ln(x^2 + 1) + C
- arcosh x + C
- artanh x + C
- arsinh x + C
-
What is the integral of 1/sqrt(x^2 - 1) for x > 1?
- arsinh x + C
- -arcosh x + C
- arcosh x + C
- artanh x + C
-
Which expression equals the integral of 1/sqrt(x^2 + a^2) dx?
- ln(x + sqrt(x^2 + a^2)) + C
- ln(x - sqrt(x^2 + a^2)) + C
- ln(x + sqrt(x^2 - a^2)) + C
- (1/a) ln(x^2 + a^2) + C
-
Find the integral of 1/sqrt(x^2 + 4) dx.
- arcosh(x/2) + C
- arsinh(x/2) + C
- (1/2) arsinh(x/2) + C
- arsinh x + C
-
Find the integral of 1/sqrt(4x^2 + 1) dx.
- (1/2) arsinh(2x) + C
- (1/2) arsinh x + C
- 2 arsinh(2x) + C
- arsinh(2x) + C
-
Find the integral of 1/sqrt(x^2 - 9) dx for x > 3.
- arsinh(x/3) + C
- (1/3) arcosh(x/3) + C
- arcosh(x/3) + C
- arcosh x + C
-
What is the integral of sinh x with respect to x?
- sinh x + C
- tanh x + C
- -cosh x + C
- cosh x + C
-
What is the integral of cosh x with respect to x?
- sinh x + C
- ln(cosh x) + C
- cosh x + C
- -sinh x + C
-
What is the integral of tanh x with respect to x?
- ln(cosh x) + C
- ln(tanh x) + C
- sech^2 x + C
- ln(sinh x) + C
-
Evaluate the integral from 0 to 1 of 1/sqrt(x^2 + 1) dx.
- ln(1 + sqrt 2)
- ln 2
- ln(sqrt 2 - 1)
- pi/4
-
Evaluate the integral from 1 to 2 of 1/sqrt(x^2 - 1) dx.
- ln(2 - sqrt 3)
- ln(2 + sqrt 3)
- ln 2
- sqrt 3
-
Find the integral of x/sqrt(x^2 + 1) dx.
- arsinh x + C
- x arsinh x + C
- (1/2) arsinh(x^2) + C
- sqrt(x^2 + 1) + C
-
Find the integral of sinh x cosh x dx.
- (1/2) sinh(2x) + C
- sinh^2 x + C
- sinh x cosh x + C
- (1/2) sinh^2 x + C
-
Find the integral of 1/sqrt(x^2 + 2x + 2) dx.
- ln(x^2 + 2x + 2) + C
- arcosh(x + 1) + C
- arsinh x + C
- arsinh(x + 1) + C
-
Find the integral of 1/sqrt(x^2 + 6x + 10) dx.
- arcosh(x + 3) + C
- arsinh(x + 6) + C
- arsinh x + C
- arsinh(x + 3) + C
-
Evaluate the integral from 0 to sqrt 3 of 1/sqrt(x^2 + 1) dx.
- ln 3
- ln(2 + sqrt 3)
- pi/3
- ln(1 + sqrt 3)
-
Find the integral of (x + 1)/sqrt(x^2 + 1) dx.
- sqrt(x^2 + 1) + arsinh x + C
- x sqrt(x^2 + 1) + C
- sqrt(x^2 + 1) + arcosh x + C
- arsinh x + C
-
For the integral of 1/sqrt(x^2 + a^2) dx, which substitution is commonly used?
- x = a cosh u
- x = a tanh u
- x = a sinh u
- x = a sin u
-
Find the integral of 1/sqrt(x^2 - 4) dx for x > 2.
- (1/2) arcosh(x/2) + C
- arcosh(x/2) + C
- arsinh(x/2) + C
- arcosh x + C
-
Evaluate the integral from 0 to ln 2 of tanh x dx.
- ln(4/5)
- ln(5/4)
- ln 2
- ln(3/4)
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