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In this lesson, we will learn how to evaluate definite and indefinite integrals for exponential functions using different techniques.
Q1:
Determine οΈ οΉ 2 π β π₯ ο π₯ 1 0 9 π₯ d .
Q2:
Use the proper substitution to find οΈ ( 9 π₯ + 7 ) π π₯ 9 π₯ + 1 4 π₯ 2 d .
Q3:
Determine οΈ 7 3 π₯ π₯ c o s 3 π₯ s i n d .
Q4:
Determine οΈ β 5 β 5 π π β β 5 π d .
Q5:
Evaluate οΈ ( π₯ + 2 π ) π₯ 1 0 π π₯ d .
Q6:
Determine οΈ 9 π ( 7 + π ) π₯ β π₯ β π₯ 2 d .
Q7:
Use the proper substitution to find οΈ 5 π π₯ π₯ β 3 π₯ 2 d .
Q8:
Determine οΈ π₯ + 9 π π₯ π₯ 2 π₯ s i n c o s d .
Q9:
Determine οΈ π ( 7 π₯ β 2 ) π₯ 7 π₯ β 4 π₯ β 1 4 2 d .
Q10:
Determine οΈ 8 π π π₯ 7 π₯ 7 π₯ c o s d .
Q11:
Determine οΈ π π β 5 π₯ 6 π₯ 6 π₯ d by using the substitution method.
Q12:
Determine οΈ β 7 π β β 8 π + 3 π₯ π₯ π₯ d .
Q13:
Determine οΈ 8 π β π + 9 7 π π₯ 3 π₯ 2 π₯ π₯ d .
Q14:
Determine οΈ β 1 β 2 π₯ π π₯ β ο¨ ο d .
Q15:
Determine the function π if π β² β² ( π₯ ) = β 3 π + 4 π₯ π₯ s i n , π ( 0 ) = 4 , and π οΌ 3 π 2 ο = 0 .
Q16:
Determine οΈ 1 9 π + 1 9 π₯ β 2 0 π β 2 0 π₯ π₯ π₯ β 1 π β 1 π₯ π d .
Q17:
Determine οΈ β 9 π 7 π + 1 2 π₯ π₯ π₯ d .
Q18:
A cup of tea at 9 0 β C is left in a room at 2 2 β C to cool at the rate of β 1 0 . 2 π ο± ο¦ ο ο§ ο« ο degrees per minute. What is the temperature of the tea after 10 minutes to the nearest degree?
Q19:
Given that π β² β² ( π₯ ) = β 5 π + 2 π₯ 4 π₯ 5 , find π ( π₯ ) .
Q20:
Determine οΈ οΉ 3 π + 8 π₯ ο π₯ 3 0 5 π₯ d .
Q21:
Determine οΈ π ( 7 π₯ + 1 ) π₯ 7 π₯ + 2 π₯ β 1 3 2 d .
Q22:
Use the proper substitution to find οΈ β π π₯ π₯ 5 π₯ 2 d .
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