Compute Cos (x + k ) cos a dx by using substitution technique where k is a constant. [Hint: cos(A± B) = cos A cos B 7 sin A sin B] k (x cos k + In(cos x) sin k) + C x cos k – In(cos x) sin k + C ............... ..... ...... x cos k + In(cos x) sin k + C x cos k + In(cos x) + C ............

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Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: 2. Evaluate the improper integral. e COs x dx

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A: The detailed solution is given below Thank you

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Q: Which of the following is not an improper integra cos x dx 0. 1 dx cos x 0. cos x dx 0. 1 dx OUESTI…

A: Improper Integral  integrand is discontinuous at a point  in given limit

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Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

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Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

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A: the given integral is: we have to evaluate the given integral.

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Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: Given f(2) = . t2 – 1 dt 1+ cos?(t) At what value of x does the local max of f(x) occur? x =

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Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +…

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Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu