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QUESTION: 1

Solution:

cos(sin^{-1}x)/(1-x^{2})^{½}……………….(1)

t = sin^{-1} x

dt = dx/(1-x^{2})^{½}

Put the value of dt in eq(1)

= ∫cost dt

= sint + c

= sin(sin^{-1} x) + c

⇒ x + c

QUESTION: 2

Integral of sin^{5}x.cos^{2}x is:

Solution:

So Looking at this integral, we have

QUESTION: 3

Evaluate:

Solution:

xe^{x} = t

(xe^{x} + e^{x}) dx = dt

= e^{x}(x + 1) dx = dt

= ∫dt/sin^{2t}

= ∫cosec^{2t} dt

= -cot(xe^{x}) + c

QUESTION: 4

Evaluate:

Solution:

Create ((X+B) + (A-B)) in numerator and then apply Sin(a+b) formula then you will be able to solve it.

QUESTION: 5

Find the distance travelled by a car moving with acceleration given by a(t)=t^{2} + t, if it moves from t = 0 sec to t = 10 sec, if velocity of a car at t = 0sec is 40 km/hr.

Solution:

= 783.3 km

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